Predictability of the quasi-biennial oscillation

Comments

Using Stuecker's rules, a sequence such as [0.5, 0.49, 0.5, -0.5, -0.49] would be considered biennial. That's strictly [up, down, up, down, up] for five consecutive years. Yet, plot that out and it doesn't appear to be a strongly biennial. That's because there are not enough zero crossings in the sequence.

I don't understand why they aren't applying more refined spectral analysis techniques to root out these periodicities rather than taking this crude approach.

Comment Source:Using Stuecker's rules, a sequence such as [0.5, 0.49, 0.5, -0.5, -0.49] would be considered biennial. That's strictly [up, down, up, down, up] for five consecutive years. Yet, plot that out and it doesn't appear to be a strongly biennial. That's because there are not enough zero crossings in the sequence.
I don't understand why they aren't applying more refined spectral analysis techniques to root out these periodicities rather than taking this crude approach.

How good does the QBO model perform for out-of-band testing? Really good. We take the QBO range from 1953-2013 and divide it into two 30 year intervals. The first half is fit and verified in the second half, and then vice versa.

This uses the 2nd derivative of the QBO signal, which has much more fine structure to fit against. All the factors are from the aliased lunisolar forcing periods.

Comment Source:How good does the QBO model perform for out-of-band testing? Really good. We take the QBO range from 1953-2013 and divide it into two 30 year intervals. The first half is fit and verified in the second half, and then vice versa.
![qbo](http://imageshack.com/a/img907/5168/xJRcpt.png)
This uses the 2nd derivative of the QBO signal, which has much more fine structure to fit against. All the factors are from the aliased lunisolar forcing periods.

Regarding the title of this thread. Applying only the precisely known aliased lunisolar forcing factors, this is in-band training and out-of-band validation for the 70MB QBO data:

You have to look closely, but the detail is amazing. Likely not much of the QBO signal is noise.

Comment Source:Regarding the title of this thread. Applying only the precisely known aliased lunisolar forcing factors, this is in-band training and out-of-band validation for the 70MB QBO data:
![qbo70](http://imageshack.com/a/img908/715/iESEZ8.png)
You have to look closely, but the detail is amazing. Likely not much of the QBO signal is noise.

The AGW denier Richard Lindzen is considered the originator of QBO theory. Yet IMO his scientific research on that topic appears poorly constructed. And I don't really know what's up with his current thinking:

“As with any cult, once the mythology of the cult begins falling apart, instead of saying, oh, we were wrong, they get more and more fanatical. I think that’s what’s happening here. Think about it,” he said. “You’ve led an unpleasant life, you haven’t led a very virtuous life, but now you’re told, you get absolution if you watch your carbon footprint. It’s salvation!”

Read the whole thing -- see if you come to the same conclusion I have, that Lindzen has finally gone off the deep-end.

I point this out because whatever thinking Lindzen is doing now, it wasn't that impressively lucid in his prime. I have looked at his research on QBO, and it is filled with arcane mathematics that doesn't really go anywhere. The QBO is clearly not what Lindzen thought it was, and the reality is that it is truly a type of atmospheric tide and so follows from the lunisolar forcing applied.

The following figure shows the 2nd derivative of the QBO signal (top) and the QBO signal itself (bottom), using only periods supplied from the known lunisolar tidal numbers. The training interval shown is enough to provide a very good extrapolation outside that region.

"That's why I started from something physical that couldn't mislead me that way. Earth-sun distance dictates a very specific set of frequencies. The seasonal cycle and its harmonics has many possible sources. So the atmospheric and oceanic circulation can show seasonal effects for many reasons. But if they're doing something at 399 or 584 days ... well, those are quite peculiar and not pushed by the internals the climate system. "

That is precisely the approach I am taking to modeling the QBO, using precise values of lunar periods, such as 27.32158 days (and aliased values)-- and finding that even small deviations from these set values degrades the model fit. This is no different than the accuracy necessary to predict ocean tides. So the QBO is best considered as a form of atmospheric tide, which should come as no surprise to all the other researchers who have observed atmospheric tides in the past.

I’d like to point out something Lindzen said which betrays a problem with Lindzen. Talking about the statements made by the 8 MIT professors, he attempts to minimize climate change thus: “… the claim that most of the climate change since 1960 is due to human activities, refers to more than half of a change on the order of only 0.5C …” I’ve heard claims like this many times, and I always wonder: is this person deliberately misleading his readers, or is he that ignorant? You can’t even get that right?

Its going to do no good to ask MIT to cut ties to Lindzen (which is what some have suggested). The best way is to prove him wrong with good science. That's really the only way to keep progressing. Let's start with the QBO and demonstrate that Lindzen regrettably lead people down the wrong path, and that 40 some years later we can get back on the right path.

Sorry for the rant-like quality of this post, but it is really appalling to see someone like Lindzen use his position of credibility to demean people concerned about our environment like that.

Comment Source:The AGW denier Richard Lindzen is considered the [originator of QBO theory](http://people.atmos.ucla.edu/cwhung/qbo.html). Yet IMO his scientific research on that topic appears poorly constructed. And I don't really know what's up with his current thinking:
[Article titled <b>*"MIT Climate Scientist: Global Warming Believers a ‘Cult’"*</b>](http://www.breitbart.com/big-government/2015/01/21/mit-climate-scientist-global-warming-believers-a-cult/)
> “As with any cult, once the mythology of the cult begins falling apart, instead of saying, oh, we were wrong, they get more and more fanatical. I think that’s what’s happening here. Think about it,” he said. “You’ve led an unpleasant life, you haven’t led a very virtuous life, but now you’re told, you get absolution if you watch your carbon footprint. It’s salvation!”
Read the whole thing -- see if you come to the same conclusion I have, that Lindzen has finally gone off the deep-end.
I point this out because whatever thinking Lindzen is doing now, it wasn't that impressively lucid in his prime. I have looked at his research on QBO, and it is filled with arcane mathematics that doesn't really go anywhere. The QBO is clearly not what Lindzen thought it was, and the reality is that it is truly a type of atmospheric tide and so follows from the lunisolar forcing applied.
The following figure shows the 2nd derivative of the QBO signal (top) and the QBO signal itself (bottom), using only periods supplied from the known lunisolar tidal numbers. The training interval shown is enough to provide a very good extrapolation outside that region.
![qbo](http://imageshack.com/a/img907/6753/TYmlZW.png)
This week Robert Grumbine from NOAA has a post (and white paper) on the idea that [known lunisolar periods control the Chandler wobble](http://moregrumbinescience.blogspot.com/2016/01/earth-sun-distance-and-chandler-wobble.html). His premise is apparent from a response he made to a question I asked:
> "That's why I started from something physical that couldn't mislead me that way. Earth-sun distance dictates a very specific set of frequencies. The seasonal cycle and its harmonics has many possible sources. So the atmospheric and oceanic circulation can show seasonal effects for many reasons. But if they're doing something at 399 or 584 days ... well, those are quite peculiar and not pushed by the internals the climate system. "
That is precisely the approach I am taking to modeling the QBO, using precise values of lunar periods, such as 27.32158 days (and aliased values)-- and finding that even small deviations from these <b>set</b> values degrades the model fit. This is no different than the accuracy necessary to predict ocean tides. So the QBO is best considered as a form of atmospheric tide, which should come as no surprise to all the other researchers who have observed atmospheric tides in the past.
Now is the time to debunk Lindzen for all the crazy stuff he has been publishing over the years. What he is doing right now is really an embarrassment to MIT. Tamino over at the [Open Mind blog has also been questioning Lindzen](https://tamino.wordpress.com/2015/12/26/richard-lindzen-limited-understanding/).
> I’d like to point out something Lindzen said which betrays a problem with Lindzen. Talking about the statements made by the 8 MIT professors, he attempts to minimize climate change thus: “… *the claim that most of the climate change since 1960 is due to human activities, refers to more than half of a change on the order of only 0.5C* …” I’ve heard claims like this many times, and I always wonder: is this person deliberately misleading his readers, or is he that ignorant? You can’t even get that right?
Its going to do no good to ask MIT to cut ties to Lindzen (which is what some have suggested). The best way is to prove him wrong with good science. That's really the only way to keep progressing. Let's start with the QBO and demonstrate that Lindzen regrettably lead people down the wrong path, and that 40 some years later we can get back on the right path.
Sorry for the rant-like quality of this post, but it is really appalling to see someone like Lindzen use his position of credibility to demean people concerned about our environment like that.

The correlation of the QBO timeseries with aliased lunisolar forcing is startlingly good, but shouldn't come as a surprise. This paper by Chinese researchers lays out some rationale and some of their own supporting evidence

"Studies of atmospheric tides also deal with global-scale periodic oscillations of the atmosphere. According to current tidal theories (Chapman and Lindzen, 1970; Forbes el al., 2003; Hagan et al., 2003; Hagan and Forbes, 2003; Lindzen, 2005), atmospheric tides are excited primarily by the Sun's heating of the atmosphere, whereas ocean tides are excited primarily by the Moon's gravitational pull."

This is a well-written paper and it essentially raises the question as to why atmospheric behavior doesn't demonstrate lunar tides but only the solar tides that Lindzen has advocated for over 40 years.

The answer is straightforward when you consider that likely no one has considered the case whereby the lunar forcing pumps the yearly solar forcing, such that the multiplicative effect will create the aliasing needed to generate the required forcing frequency to match the QBO observations.

Say that the lunar forcing signal is lunar(t) and the solar is solar(t) where

$ lunar(t) = \Sigma k_i sin(\nu_i t +\phi_i) $

and

$ solar(t) = \Sigma c_m sin(2\pi m t +\psi_m) $

The latter is likely a sharp seasonal signal that cuts in and out abruptly, so requires higher harmonics than yearly (including the biannual, 1/3 etc). The result of pumping is that lunar(t) and solar(t) are multiplicative, so that

$ r(t) = lunar(t) \cdot solar(t) $

Taking the Fourier transform of the result generates a convolution of the frequency terms in that space, so that result is a sum of Dirac delta terms in frequency space.

What this implies is that the original high frequency lunar sinusoids are replaced by the lower frequency seasonally aliased signals that the atmosphere can physically respond to. In other words, this downshift in frequency allows the inertial mass of the upper atmosphere to respond to a more sustained forcing, instead of the rapid fluctuations of the physical lunar cycle.

So therefore we find values of $ \nu_i - 2\pi m $ that are in a range corresponding to physical periods of 0.5 to 3 years -- i.e. that of the QBO. Of course these are higher harmonics (10 - 13) in the yearly signal, but that is what is required to represent sudden seasonal transitions. The idea being that specific intervals of the season will amplify the lunar gravitational pull at that moment to get the QBO winds in motion along a certain longitudinal (i.e. meridional) direction.

This should have been obvious to anyone that has looked at the QBO signal over the years, apart from one aspect -- the aliasing of the harmonics of the fundamental frequency are not harmonics of the aliased fundamental. What that means is that the resultant waveform doesn't necessarily look pretty, as in a harmonic overturn would sound pleasing to the ear. Instead, the frequencies are precise, but not related as multiples, but replaced by $2\pi$ shifts. So that if you are looking at the frequency power spectrum expecting to find multiples of a fundamental frequency, you won't find any. Instead, you will see frequencies all over the map and think that there is a chaotic nature to the QBO. That's what I think stymied researchers all this time.

The way to see this detail is to take the second derivative of the QBO time series. We know that the QBO is a wave so that it must somehow respond to a wave-equation:

$ QBO''(t) + \omega_0^2 QBO(t) = r(t) $

where the RHS is the lunisolar forcing. If we take the premise that the QBO signal is a forced response (just like ocean tides are), then the r(t) forcing will show up in the second derivative of QBO(t) (as well as QBO itself).

So when we reconstruct the signal shown in the chart above in comment #104, and find precise registration with the aliased lunar periods set up as a Fourier series, then in all likelihood, this is the only model that could conceivably produce that fixed cyclic behavior.

I quoted Robert Grumbine who just this week echoed that assertion:

"But if they're doing something at 399 or 584 days ... well, those are quite peculiar and not pushed by the internals the climate system."

and years before that Lindzen himself stated that

"Lunar tides are especially well suited to such studies since it is unlikely that lunar periods could be produced by anything other than the lunar tidal potential. "

But Lindzen never considered aliased lunar periods, which is what this is all about. That explains why Lindzen spent 40+ years of his career gong down the rabbit hole of increasingly complicated theory to explain QBO, while the simplest solution was always in plain sight. What Li et al say in the paper really holds -- some other approach was needed to root out the lunar signal:

"This is the way the term "atmospheric tide" is described and explained in textbooks, dictionaries and encyclopedias; however, the atmospheric tide produced by lunar gravitation pull has never been observed in the Earth's atmosphere, whereas the tides in oceans and the Earth's crust, excited by lunar gravitation pull, appear so strong."

Since Lindzen is based in Boston, I would be curious to find out how he would like them apples.

Comment Source:The correlation of the QBO timeseries with aliased lunisolar forcing is startlingly good, but shouldn't come as a surprise. This paper by Chinese researchers lays out some rationale and some of their own supporting evidence
> Li, Guoqing, Haifeng Zong, and Qingyun Zhang. *"27.3-day and average 13.6-day periodic oscillations in the earth’s rotation rate and atmospheric pressure fields due to celestial gravitation forcing."* Advances in Atmospheric Sciences 28 (2011): 45-58.
> "Studies of atmospheric tides also deal with global-scale periodic oscillations of the atmosphere. According to current tidal theories (Chapman and <font color=red>Lindzen</font>, 1970; Forbes el al., 2003; Hagan et al., 2003; Hagan and Forbes, 2003; <font color=red>Lindzen</font>, 2005), atmospheric tides are excited primarily by the Sun's heating of the atmosphere, whereas ocean tides are excited primarily by the Moon's gravitational pull."
![liFig](http://imageshack.com/a/img907/6135/JQ4s7o.gif)
This is a well-written paper and it essentially raises the question as to why atmospheric behavior doesn't demonstrate lunar tides but only the solar tides that <font color=red>Lindzen</font> has advocated for over 40 years.
The answer is straightforward when you consider that likely no one has considered the case whereby the lunar forcing *pumps* the yearly solar forcing, such that the multiplicative effect will create the aliasing needed to generate the required forcing frequency to match the QBO observations.
Say that the lunar forcing signal is *lunar(t)* and the solar is *solar(t)* where
$ lunar(t) = \Sigma k_i sin(\nu_i t +\phi_i) $
and
$ solar(t) = \Sigma c_m sin(2\pi m t +\psi_m) $
The latter is likely a sharp seasonal signal that cuts in and out abruptly, so requires higher harmonics than yearly (including the biannual, 1/3 etc). The result of pumping is that *lunar(t)* and *solar(t)* are multiplicative, so that
$ r(t) = lunar(t) \cdot solar(t) $
Taking the Fourier transform of the result generates a convolution of the frequency terms in that space, so that result is a sum of Dirac delta terms in frequency space.
$ R(\omega) = \Sigma_i \Sigma_m A_{im} \delta( \omega - (\nu_i - 2\pi m)) $
What this implies is that the original high frequency lunar sinusoids are replaced by the lower frequency seasonally aliased signals that the atmosphere can physically respond to. In other words, this downshift in frequency allows the inertial mass of the upper atmosphere to respond to a more sustained forcing, instead of the rapid fluctuations of the physical lunar cycle.
So therefore we find values of $ \nu_i - 2\pi m $ that are in a range corresponding to physical periods of 0.5 to 3 years -- i.e. that of the QBO. Of course these are higher harmonics (10 - 13) in the yearly signal, but that is what is required to represent sudden seasonal transitions. The idea being that specific intervals of the season will amplify the lunar gravitational pull at that moment to get the QBO winds in motion along a certain longitudinal (i.e. meridional) direction.
This should have been obvious to anyone that has looked at the QBO signal over the years, apart from one aspect -- the aliasing of the harmonics of the fundamental frequency are not harmonics of the aliased fundamental. What that means is that the resultant waveform doesn't necessarily look pretty, as in a harmonic overturn would sound pleasing to the ear. Instead, the frequencies are precise, but not related as multiples, but replaced by $2\pi$ shifts. So that if you are looking at the frequency power spectrum expecting to find multiples of a fundamental frequency, you won't find any. Instead, you will see frequencies all over the map and think that there is a chaotic nature to the QBO. That's what I think stymied researchers all this time.
The way to see this detail is to take the second derivative of the QBO time series. We know that the QBO is a wave so that it must somehow respond to a wave-equation:
$ QBO''(t) + \omega_0^2 QBO(t) = r(t) $
where the RHS is the lunisolar forcing. If we take the premise that the QBO signal is a *forced* response (just like ocean tides are), then the *r(t)* forcing will show up in the second derivative of *QBO(t)* (as well as QBO itself).
So when we reconstruct the signal shown in [the chart above in comment #104](#Comment_15123), and find precise registration with the aliased lunar periods set up as a Fourier series, then in all likelihood, this is the *only model* that could conceivably produce that fixed cyclic behavior.
I quoted Robert Grumbine who just this week echoed that assertion:
> "But if they're doing something at 399 or 584 days ... well, those are quite peculiar and not pushed by the internals the climate system."
and years before that Lindzen himself stated that
> "Lunar tides are especially well suited to such studies since it is unlikely that <b>lunar periods could be produced by anything other than the lunar tidal potential</b>. "
But Lindzen never considered *aliased* lunar periods, which is what this is all about. That explains why Lindzen spent 40+ years of his career gong down the rabbit hole of increasingly complicated theory to explain QBO, while the simplest solution was always in plain sight. What Li *et al* say in the paper really holds -- some other approach was needed to root out the lunar signal:
> "This is the way the term "atmospheric tide" is described and explained in textbooks, dictionaries and encyclopedias; however, the atmospheric tide produced by lunar gravitation pull has never been observed in the Earth's atmosphere, whereas the tides in oceans and the Earth's crust, excited by lunar gravitation pull, appear so strong."
Since Lindzen is based in Boston, I would be curious to find out how he would like them apples.

Here are a couple of sensitivity analyses of the QBO model to support the last comment

First a multiple regression training/validation evaluation of the model wrt the second derivative of QBO. The bottom panel only misses the phase over two intervals shown with yellow fill.

Then an evaluation over the entire interval, whereby I change the fundamental lunar monthly periods from their nominally fixed values by a fraction of a percent and then re-evaluate the multiple regression correlation between data and model. The top set is the QBO and the bottom set is second derivative of QBO.

Apart from the weaker evection term, the CC responses align with the lunar periods very sharply. That is consistent with the machine learning results that I essentially started with.

Where to go from here?

People are getting excited about the possibility of a Planet 9 in our solar system -- How did we miss Planet 9? -- which "has been inferred by its gravitational influence on other icy bodies out there in the farthest reaches of our solar system".

The writer has a good analogy:

"It's like seeing a disturbance on the surface of water but not knowing what caused it. Perhaps it was a jumping fish, a whale or a seal. Even though you didn't actually see it, you could make an informed guess about the size of the object and its location by the nature of the ripples in the water."

By comparison, that's all the QBO is -- a set of ripples with a characteristic pattern of whose origin can only be deduced though informed guessing.

So the elephant-in-the-room question is how could we miss what may be a clear gravitational forcing effect right in our own backyard? If this model pans out, I see a future article titled "How did we miss QBO?".

According to Wikipedia : "In 1609 Johannes Kepler correctly suggested that the gravitation of the Moon causes the tides, basing his argument upon ancient observations and correlations. It was originally mentioned in Ptolemy's Tetrabiblos as having derived from ancient observation."

Then in the 1950s, the QBO was discovered. In 1970 Lindzen was recognized for having the first theory of QBO, but this theory did not include the Moon as a forcing.

But now, all indications (from unbiased machine learning results to a plausible physical model) point to the Moon as having a dominant effect on the periodicity of the QBO behavior. If this is indeed true, then all the climate models would need to include this new information. Over at Robert Grumbine's blog, this discussion is taking place -- one commenter said if external lunisolar forcings are playing a role, then "This might indeed be an essential part for simulating natural variability in climate models."

So what will it take to falsify the physics of this QBO model as it stands? In comparison, what will it take to falsify the ocean tidal model? I really don't see a fundamental difference between the two at this stage.

Comment Source:Here are a couple of sensitivity analyses of the QBO model to support [the last comment](#Comment_15124)
First a multiple regression training/validation evaluation of the model wrt the second derivative of QBO. The bottom panel only misses the phase over two intervals shown with yellow fill.
![extrapolation](http://imageshack.com/a/img907/5050/CMo0fK.png)
Then an evaluation over the entire interval, whereby I change the fundamental lunar monthly periods from their nominally fixed values by a fraction of a percent and then re-evaluate the multiple regression correlation between data and model. The top set is the QBO and the bottom set is second derivative of QBO.
![sens](http://imageshack.com/a/img911/5238/fBNR2Q.png)
Apart from the weaker evection term, the CC responses align with the lunar periods very sharply. That is consistent with the machine learning results that I essentially started with.
---
Where to go from here?
People are getting excited about the possibility of a Planet 9 in our solar system -- [How did we miss Planet 9?](http://www.cbc.ca/news/technology/planet-9-bob-macdonald-1.3414268) -- which *"has been inferred by its gravitational influence on other icy bodies out there in the farthest reaches of our solar system"*.
The writer has a good analogy:
> "It's like seeing a disturbance on the surface of water but not knowing what caused it. Perhaps it was a jumping fish, a whale or a seal. Even though you didn't actually see it, you could make an informed guess about the size of the object and its location by the nature of the ripples in the water."
By comparison, that's all the QBO is -- a set of ripples with a characteristic pattern of whose origin can only be deduced though informed guessing.
So the elephant-in-the-room question is how could we miss what may be a clear gravitational forcing effect right in our own backyard? If this model pans out, I see a future article titled "How did we miss QBO?".
According to Wikipedia : *"In 1609 Johannes Kepler correctly suggested that the gravitation of the Moon causes the tides, basing his argument upon ancient observations and correlations. It was originally mentioned in Ptolemy's Tetrabiblos as having derived from ancient observation."*
Then in the 1950s, the QBO was discovered. In 1970 Lindzen was recognized for having the first theory of QBO, but this theory did not include the Moon as a forcing.
But now, all indications (from unbiased machine learning results to a plausible physical model) point to the Moon as having a dominant effect on the periodicity of the QBO behavior. If this is indeed true, then all the climate models would need to include this new information. Over at Robert Grumbine's blog, this discussion is taking place -- one commenter said if external lunisolar forcings are playing a role, then [*"This might indeed be an essential part for simulating natural variability in climate models."*](http://moregrumbinescience.blogspot.com/2016/01/earth-sun-distance-and-chandler-wobble.html)
So what will it take to falsify the physics of this QBO model as it stands? In comparison, what will it take to falsify the ocean tidal model? I really don't see a fundamental difference between the two at this stage.

Here are the luni-solar tidal coefficients that go in to the QBO fit of comment #106

The upper rows are the main lunar terms, showing the aliased harmonics along the columns.
The bottom row are the main solar terms, which are not aliased.

The various terms contribute differing magnitudes to the multiple regression, but have a common behavior in that if these periods vary by a fraction of a percent, the fit deteriorates as shown in the previous comment.

That behavior is no different than what happens in a tidal analysis -- the individual tidal factors are fixed in period but the magnitudes change.

The values in the table are available from RD Ray's paper, or from tidal constituent tables.

The world that this opens up is fascinating. It's been 60 years since the QBO was first measured, yet we may be finding this precise correlation with the luni-solar periods only now.

Comment Source:Here are the luni-solar tidal coefficients that go in to the QBO fit of [comment #106](#Comment_15125)
![table](http://imageshack.com/a/img907/4404/AkqGKm.png)
The upper rows are the main lunar terms, showing the aliased harmonics along the columns.
The bottom row are the main solar terms, which are not aliased.
The various terms contribute differing magnitudes to the multiple regression, but have a common behavior in that if these periods *vary by a fraction of a percent*, the fit deteriorates as shown in the previous comment.
That behavior is no different than what happens in a tidal analysis -- the individual tidal factors are fixed in period but the magnitudes change.
The values in the table are available from RD Ray's paper, or from tidal constituent tables.
[1]R. D. Ray and S. Y. Erofeeva, *“Long‐period tidal variations in the length of day,”* Journal of Geophysical Research: Solid Earth, vol. 119, no. 2, pp. 1498–1509, 2014.
The world that this opens up is fascinating. It's been 60 years since the QBO was first measured, yet we may be finding this precise correlation with the luni-solar periods only now.

In Comment #107 I added a weak but very sharp contribution of 0.56372 years to the Solar row of the QBO model. This corresponds to a known cycle of 205.9 days, which is described here, and the figure below.

"Figure 4-6 shows that the eccentricity reaches a maximum when the major axis of the lunar orbit is pointed directly towards or directly away from the Sun (angles of 0° and 180°, respectively). This occurs at a mean interval of 205.9 days, which is somewhat longer than half a year because of the eastward shift of the major axis. The eccentricity reaches a minimum when the major axis of the lunar orbit is perpendicular to the Sun (angles of 90° and 270°)."

This makes it a luni-solar mix but is classified as solar in Ray's table. The other feature in that figure (see the arrow labeled "instantaneous eccentricity") is the faster Evection cycle of 31.8 days, which also features in the QBO fit as an aliased signal, but not quite as sharply. That's one that the Eureqa machine learning picked up in comment #67 as an aliased signal.

There is another tidal period that curiously doesn't show up in Ray's table but is in other tidal tables. That is at ~0.53 yr = 193.6 days, which is based on the nodal extent instead of anomalistic extent.

Another new feature is the 0.24254 year cycle which corresponds to the synodic season of 88.59 = 3*29.53 days, where 29.53 days is the duration of the lunar synodic month. A "season" is 3 months so that's why I referred to it as a synodic season. The way I found this cycle is by doing an FFT of the residual of the QBT'' fit. This shows up very sharply, but the explanation for it may be a bit involved.

This passage may help, from "Exploring Ancient Skies: A Survey of Ancient and Cultural Astronomy" by David H. Kelley, Eugene F. Milone

After the inclusion of all these factors, there is still a few percent of the signal taken up by splitting of the tropical 27.32 day period. According to Ray's table, they have values such as 27.667, 27.443, 27.093, and 26.985 days. These likely do contribute as factors, since the power spectrum of the residual does show 4 remaining peaks at about these locations (after aliasing) -- but you have to be careful about fitting with these factors so close to the white noise floor.

2nd derivative fit

Comment Source:In [Comment #107](#Comment_15128) I added a weak but very sharp contribution of 0.56372 years to the Solar row of the QBO model. This corresponds to a known cycle of 205.9 days, which is described [here](http://eclipse.gsfc.nasa.gov/SEhelp/moonorbit.html), and the figure below.
![orbit](http://eclipse.gsfc.nasa.gov/SEhelp/image/Fig4-6b.png)
> "Figure 4-6 shows that the eccentricity reaches a maximum when the major axis of the lunar orbit is pointed directly towards or directly away from the Sun (angles of 0° and 180°, respectively). This occurs at a mean interval of 205.9 days, which is somewhat longer than half a year because of the eastward shift of the major axis. The eccentricity reaches a minimum when the major axis of the lunar orbit is perpendicular to the Sun (angles of 90° and 270°)."
This makes it a luni-solar mix but is classified as solar in Ray's table. The other feature in that figure (see the arrow labeled "instantaneous eccentricity") is the faster Evection cycle of 31.8 days, which also features in the QBO fit as an aliased signal, but not quite as sharply. That's one that the Eureqa machine learning picked up in [comment #67](#Comment_14919) as an aliased signal.
There is another tidal period that curiously doesn't show up in Ray's table but is in other tidal tables. That is at ~0.53 yr = 193.6 days, which is based on the nodal extent instead of anomalistic extent.
[NOAA Special Publication NOS CO-OPS 3 Tidal Analysis and Prediction Bruce B. Parker, Ph.D. Silver Spring, Maryland July 2007](http://tidesandcurrents.noaa.gov/publications/Tidal_Analysis_and_Predictions.pdf)
Another new feature is the 0.24254 year cycle which corresponds to the synodic season of 88.59 = 3*29.53 days, where 29.53 days is the duration of the lunar synodic month. A "season" is 3 months so that's why I referred to it as a synodic season. The way I found this cycle is by doing an FFT of the residual of the QBT'' fit. This shows up very sharply, but the explanation for it may be a bit involved.
This passage may help, from "Exploring Ancient Skies: A Survey of Ancient and Cultural Astronomy" by David H. Kelley, Eugene F. Milone
![moon](http://imageshack.com/a/img903/1527/lAMFUL.gif)
After the inclusion of all these factors, there is still a few percent of the signal taken up by splitting of the tropical 27.32 day period. According to Ray's table, they have values such as 27.667, 27.443, 27.093, and 26.985 days. These likely do contribute as factors, since the power spectrum of the residual does show 4 remaining peaks at about these locations (after aliasing) -- but you have to be careful about fitting with these factors so close to the white noise floor.
2nd derivative fit
![all](http://imageshack.com/a/img633/9729/jbBWM4.png)

Ordinarily, if you take a time series and differentiate it twice or more w/o applying a filter you end up with a noisy mess.

Not so with the QBO time series. Apparently every inflection point represents a contribution from a set of luni-solar factors. So what the double differentiation does is reveal these seemingly chaotic cycles running on top of the ~28 month QBO period.

These sinusoidal factors are aliased harmonics of the lunar tidal signals and harmonics of the yearly solar signal. They all need to be precise to a number of significant digits or the fit will degrade rapidly over the course of 60+ years. As far as the factors are concerned, look them up in a tide analysis handbook, apply yearly aliasing as needed and then let the multiple regression take care of it. Minus the aliasing, that is exactly how modern tidal prediction algorithms work. The only difference is that these tidal cycles occur in the stratosphere, not in the ocean.

The idea of tidal analysis is straight-forward Fourier series, but the number of factors involved (nodal, anomalistic, etc) means that you can't settle for just a couple, but need to incorporate each significant factor into the set.

This is what it looks like along a single timeline

No one can make the accusation that filtering is concealing certain behaviors, since there is no filtering applied!

Comment Source:Ordinarily, if you take a time series and differentiate it twice or more w/o applying a filter you end up with a noisy mess.
Not so with the QBO time series. Apparently every inflection point represents a contribution from a set of luni-solar factors. So what the double differentiation does is reveal these seemingly chaotic cycles running on top of the ~28 month QBO period.
![qbo](http://imageshack.com/a/img907/5880/z1Dq4N.png)
These sinusoidal factors are aliased harmonics of the lunar tidal signals and harmonics of the yearly solar signal. They all need to be precise to a number of significant digits or the fit will degrade rapidly over the course of 60+ years. As far as the factors are concerned, look them up in a tide analysis handbook, apply yearly aliasing as needed and then let the multiple regression take care of it. Minus the aliasing, that is exactly how modern tidal prediction algorithms work. The only difference is that these tidal cycles occur in the stratosphere, not in the ocean.
The idea of tidal analysis is straight-forward Fourier series, but the number of factors involved (nodal, anomalistic, etc) means that you can't settle for just a couple, but need to incorporate each significant factor into the set.
This is what it looks like along a single timeline
![one](http://imageshack.com/a/img633/9295/rsQ8bD.png)
No one can make the accusation that filtering is concealing certain behaviors, since there is no filtering applied!

I noticed that my computer was bogged down and then I realized that Eureqa had been grinding away for several days, generating over 10 trillion formula evaluations on a QBO time series experiment I had set up.

I had let it loose on a short 16 year interval of the QBO 30 hPa time series, looking at the 2nd derivative.

What it found was neat, as it essentially validated the Draconic row in the table I presented earlier.

Without any prompting, Eureqa found the exact same set of aliased harmonics that should occur if Draconic month aliasing was occurring.

which is well within any phase propagation error in a 16 year interval.

For completeness, another factor Eureqa selected, 1598.2936cos(0.07492t^2), was a spread around 0.7 years when unaliased. That's a bit complicated as it looks as if the frequency changes slightly over the interval. Yet, this is acceptable as other periods around 0.7 occur according to the table. Since this is a second derivative, it is detecting with an emphasis on these shorter periods as well. The 2.363 factor was the final piece according to the Pareto front.

The other was the known 0.53 year tidal factor 857.8cos(11.9297t)

So that is what Eureqa found after trillions of trials, a nice validation of the lunar aliasing mechanism.

Comment Source:I noticed that my computer was bogged down and then I realized that Eureqa had been grinding away for several days, generating over 10 trillion formula evaluations on a QBO time series experiment I had set up.
![EQ1](http://imageshack.com/a/img905/2758/2lQoRB.jpg)
I had let it loose on a short 16 year interval of the QBO 30 hPa time series, looking at the 2nd derivative.
![EQ2](http://imageshack.com/a/img912/1410/pX5ZeD.jpg)
What it found was neat, as it essentially validated the Draconic row in the table I presented earlier.
![table](http://imageshack.com/a/img907/4404/AkqGKm.png)
Without any prompting, Eureqa found the exact same set of aliased harmonics that should occur if Draconic month aliasing was occurring.
<pre>
2.363 and 0.6939 -- 2902.193*sin(3.19778396*t)*cos(5.8565998*t)
0.413966 -- 1032.57681*cos(15.1785856*t)
</pre>
These are the comparisons:
2.363 vs. 2.366 expected
0.6939 vs. 0.7029 expected
0.413966 vs. 0.41278 expected
which is well within any phase propagation error in a 16 year interval.
For completeness, another factor Eureqa selected, 1598.2936*cos(0.07492*t^2), was a spread around 0.7 years when unaliased. That's a bit complicated as it looks as if the frequency changes slightly over the interval. Yet, this is acceptable as other periods around 0.7 occur according to the table. Since this is a second derivative, it is detecting with an emphasis on these shorter periods as well. The 2.363 factor was the final piece according to the Pareto front.
The other was the known 0.53 year tidal factor 857.8*cos(11.9297*t)
So that is what Eureqa found after trillions of trials, a nice validation of the lunar aliasing mechanism.

This is a well-written paper and it essentially raises the question as to why atmospheric behavior doesn't demonstrate lunar tides but only the solar tides that Lindzen has advocated for over 40 years.

Are you sure that lunar tides dont play a role in Lindzens models?

The article you linked to is not too well to understand but he wrote:

The study assumes that tropical Kelvin wave is the forcing of the QBO westerly winds and tropical mixed Rossby-gravity wave is the forcing of the QBO easterly winds. However, tropical gravity wave and extratropical planetary wave are taken into account.
This model includes gravity wave drag above 35 Km, the annual cycle in the incoming solar flux, lower level forcing as Holton-Lindzen(1972) model, and extratropical planetary waves.

I dont know what "gravity wave drag" is and only a little about those Kelvin waves and Rossby-gravity, but all those three might have implicitly a lunar component, since they seem to be amongst others only secondary features of planetary motions.

Comment Source:>This is a well-written paper and it essentially raises the question as to why atmospheric behavior doesn't demonstrate lunar tides but only the solar tides that Lindzen has advocated for over 40 years.
Are you sure that lunar tides dont play a role in Lindzens models?
The article you linked to is not too well to understand but he wrote:
> The study assumes that tropical Kelvin wave is the forcing of the QBO westerly winds and tropical mixed Rossby-gravity wave is the forcing of the QBO easterly winds. However, tropical gravity wave and extratropical planetary wave are taken into account.
This model includes gravity wave drag above 35 Km, the annual cycle in the incoming solar flux, lower level forcing as Holton-Lindzen(1972) model, and extratropical planetary waves.
I dont know what "gravity wave drag" is and only a little about those Kelvin waves and Rossby-gravity, but all those three might have implicitly a lunar component, since they seem to be amongst others only secondary features of planetary motions.

Lindzen has said over and over for 40+ years that only solar tides play a role in the QBO. And these solar tides are I think mainly related to seasonal radiation changes and not gravity. Lindzen brought up lunar tides but then dismissed the idea in a few places. Here is a typical quote of his:

" 5. Lunar semidiurnal tide : One rationale for studying tides is that they are motion systems for which we know the periods perfectly, and the forcing almost as well (this is certainly the case for gravitational tides). Thus, it is relatively easy to isolate tidal phenomena in the data, to calculate tidal responses in the atmosphere, and to compare the two. Briefly, conditions for comparing theory and observation are relatively ideal. Moreover, if theory is incapable of explaining observations for such a simple system, we may plausibly be concerned with our ability to explain more complicated systems. Lunar tides are especially well suited to such studies since it is unlikely that lunar periods could be produced by anything other than the lunar tidal potential. The only drawback in observing lunar tidal phenomena in the atmosphere is their weak amplitude, but with sufficiently long records this problem can be overcome [viz. discussion in Chapman and Lindaen (1970)] at least in analyses of the surface pressure oscillation. " -- from Lindzen, Richard S., and Siu-Shung Hong. "Effects of mean winds and horizontal temperature gradients on solar and lunar semidiurnal tides in the atmosphere." Journal of the Atmospheric Sciences 31.5 (1974): 1421-1446.

Note the italicized sentence. He brings up the possibility of lunar tides, but then dismisses it. Lunar forcing never really comes up in his theory for QBO. I have looked at the CMIP models that apparently can model the QBO and there is no lunar forcing anywhere to be found.

So what I did to completely debunk Lindzen is to use his own words against him. I essentially isolated the forcing in the QBO data and compared against the known model for lunar tidal gravitational forcing. Just like he said it should be done. Unfortunately, Lindzen never did understand how lunar forcing could be aliased against the yearly solar forcing. In my previous comment, I showed how even a dumb machine learning tool could isolate the lunar periods, for cripes sake! As Lindzen said "it is unlikely that lunar periods could be produced by anything other than the lunar tidal potential." He is forced to eat his words on this one!

"I dont know what "gravity wave drag" is and only a little about those Kelvin waves and Rossby-gravity, but all those three might have implicitly a lunar component, since they seem to be amongst others only secondary features of planetary motions."

Certainly. But why is the lunar forcing not explicitly included in any of the CMIP climate models? With my approach, we have a completely deterministic mechanism that will allow one to predict the precise nature of every QBO oscillation. Again, why is no one else doing this, if gravity forcing is considered important ???

That's a rhetorical question, because I know that proposals to NASA JPL recommending the study of lunar and planetary influences have been rejected. Former JPL researchers are going off on their own to look at the research topic, see MoonClimate.org for example. Also, Robert Grumbine, who I believe works at NOAA, is starting to look at these mechanisms at his personal blog -- http://moregrumbinescience.blogspot.com . I am sure this is not funded by NOAA, as he is posting his white papers without peer-review.

Comment Source:> "Are you sure that lunar tides dont play a role in Lindzens models?"
Lindzen has said over and over for 40+ years that *only solar tides* play a role in the QBO. And these solar tides are I think mainly related to seasonal radiation changes and not gravity. Lindzen brought up lunar tides but then dismissed the idea in a few places. Here is a typical quote of his:
> " 5. Lunar semidiurnal tide : One rationale for studying tides is that they are motion systems for which we know the periods perfectly, and the forcing almost as well (this is certainly the case for gravitational tides). Thus, it is relatively easy to isolate tidal phenomena in the data, to calculate tidal responses in the atmosphere, and to compare the two. Briefly, conditions for comparing theory and observation are relatively ideal. Moreover, if theory is incapable of explaining observations for such a simple system, we may plausibly be concerned with our ability to explain more complicated systems. *Lunar tides are especially well suited to such studies since it is unlikely that lunar periods could be produced by anything other than the lunar tidal potential.* The only drawback in observing lunar tidal phenomena in the atmosphere is their weak amplitude, but with sufficiently long records this problem can be overcome [viz. discussion in Chapman and Lindaen (1970)] at least in analyses of the surface pressure oscillation. " -- from Lindzen, Richard S., and Siu-Shung Hong. "Effects of mean winds and horizontal temperature gradients on solar and lunar semidiurnal tides in the atmosphere." Journal of the Atmospheric Sciences 31.5 (1974): 1421-1446.
Note the italicized sentence. He brings up the possibility of lunar tides, but then dismisses it. Lunar forcing never really comes up in his theory for QBO. I have looked at the CMIP models that apparently can model the QBO and there is no lunar forcing anywhere to be found.
So what I did to completely debunk Lindzen is to use his own words against him. I essentially isolated the forcing in the QBO data and compared against the known model for lunar tidal gravitational forcing. Just like he said it should be done. Unfortunately, Lindzen never did understand how lunar forcing could be aliased against the yearly solar forcing. In my previous comment, I showed how even a dumb machine learning tool could isolate the lunar periods, for cripes sake! As Lindzen said *"it is unlikely that lunar periods could be produced by anything other than the lunar tidal potential."* He is forced to eat his words on this one!
> "I dont know what "gravity wave drag" is and only a little about those Kelvin waves and Rossby-gravity, but all those three might have implicitly a lunar component, since they seem to be amongst others only secondary features of planetary motions."
Certainly. But why is the lunar forcing not explicitly included in any of the [CMIP climate models](http://cmip-pcmdi.llnl.gov/)? With my approach, we have a completely deterministic mechanism that will allow one to predict the precise nature of every QBO oscillation. Again, why is no one else doing this, if gravity forcing is considered important ???
That's a rhetorical question, because I know that proposals to NASA JPL recommending the study of lunar and planetary influences have been rejected. Former JPL researchers are going off on their own to look at the research topic, see [MoonClimate.org](http://MoonClimate.org) for example. Also, Robert Grumbine, who I believe works at NOAA, is starting to look at these mechanisms at his personal blog -- [http://moregrumbinescience.blogspot.com](http://moregrumbinescience.blogspot.com/) . I am sure this is not funded by NOAA, as he is posting his white papers without peer-review.

That's a rhetorical question, because I know that proposals to NASA JPL recommending the study of lunar and planetary influences have been rejected.

Well whatsoever. Planetary motions are certainly a trigger for all sorts of climate events. Major questions which arise here are though how big is the impact of what, what are the major involved mechanisms which lead to what and how blurry is the influence of the corresponding factors.
Like I find it not too astonishing that the moon plays a role in your computations, it is a bit strange though that it appears in this way in such a simple oscillator model as you claimed. But lets assume it is so - as said I also dont feel like checking your equations-then the questions: what exactly are the involved mechanisms? Why should that be so? are not explained by that model. In the same vein I am astonished that Grumbine suggests that "the atmosphere-ocean variability near the Chandler Wobble period, among others, is paced by variation in earth-sun distance". I dont know but I would have first suspected that the Chandler Wobble itself might be a gravitational effect linked to the earthsunmoonorbits (and in particular sun-earth distance) and that the climate variabilities are then more a kind of consequence of the wobblesearthorbitsrotations, which doesnt rule out that they may exert influence via a kind of feedback.

Comment Source:>That's a rhetorical question, because I know that proposals to NASA JPL recommending the study of lunar and planetary influences have been rejected.
Well whatsoever. Planetary motions are certainly a trigger for all sorts of climate events. Major questions which arise here are though how big is the impact of what, what are the major involved mechanisms which lead to what and how blurry is the influence of the corresponding factors.
Like I find it not too astonishing that the moon plays a role in your computations, it is a bit strange though that it appears in this way in such a simple oscillator model as you claimed. But lets assume it is so - as said I also dont feel like checking your equations-then the questions: what exactly are the involved mechanisms? Why should that be so? are not explained by that model. In the same vein I am astonished that <a href="http://moregrumbinescience.blogspot.de/2016/01/earth-sun-distance-and-chandler-wobble.html">Grumbine suggests</a> that "the atmosphere-ocean variability near the Chandler Wobble period, among others, is paced by variation in earth-sun distance". I dont know but I would have first suspected that the Chandler Wobble itself might be a gravitational effect linked to the earthsunmoonorbits (and in particular sun-earth distance) and that the climate variabilities are then more a kind of consequence of the wobblesearthorbitsrotations, which doesnt rule out that they may exert influence via a kind of feedback.

"In the same vein I am astonished that Grumbine suggests that "the atmosphere-ocean variability near the Chandler Wobble period, among others, is paced by variation in earth-sun distance". I dont know but I would have first suspected that the Chandler Wobble itself might be a gravitational effect linked to the earthsunmoonorbits (and in particular sun-earth distance) and that the climate variabilities are then more a kind of consequence of the wobblesearthorbitsrotations, which doesnt rule out that they may exert influence via a kind of feedback."

Might have to split this out into another thread, because there is an amazing coincidence between my model of luni-solar driven QBO and a similar application to the Chandler wobble. Grumbine thinks the Chandler wobble is solar+planetary influence, but I argue that it is solar+lunar influence based on the following calculation, which I described on my blog yesterday:

This idea essentially relates that the modulation of the yearly solar orbit (365.242 days) with the draconic (or nodal) lunar month of 27.21222 days sets up the perfect cyclic forcing for the 433 +/- 1.1 days Chandler wobble period.

Think in terms of the maximum declination of (1) the moon with respect to the equator along with (2) the maximum declination of the sun with respect to the equator. For (1) this happens once every ½ of the 27.2122 day nodal cycle or 13.60611 days and for (2) this happens twice a year (once for the southern hemisphere summer and once for the northern hemisphere summer).

Calculating this out, the closest aliased value is 2π(365.242/13.606)−52π = 5.303 rads/year, equivalent to a period of 432.77 days. That is close to the generally accepted value of 433 days for the wobble.

The way to think about this is of a spinning top (the Earth) being tugged at by a force that is simultaneously rotating obliquely about that axis (the Moon). If the Moon was strictly rotating concentrically about the equator, no wobble would be observed. But since the Moon follows a path with varying levels of declination about the equator, one would naively imagine that this would induce a slight wobbling force to the Earth's axis. That's what they refer to as a nutation, i.e. a wobbling rotation. Yet this idea is largely dismissed in the literature, suggesting that the Chandler wobble period is a "free" rotation arising more from a resonance condition involving the density and other characteristics of the Earth.

I would take their word for it if the wobble period of 432.7 days calculated from a first-principle trig argument didn't align so closely with the measured 433 days. Don't you hate when that happens? :)

So is the wobble forced or is it free? Grumbine says the former but lays it on solar+planetary forcing, whereas I think the 433 day period points to the forcing as predominately solar+lunar. I posted a comment to Grumbine's blog and will see how he responds.

Comment Source:> "In the same vein I am astonished that Grumbine suggests that "the atmosphere-ocean variability near the Chandler Wobble period, among others, is paced by variation in earth-sun distance". I dont know but I would have first suspected that the Chandler Wobble itself might be a gravitational effect linked to the earthsunmoonorbits (and in particular sun-earth distance) and that the climate variabilities are then more a kind of consequence of the wobblesearthorbitsrotations, which doesnt rule out that they may exert influence via a kind of feedback."
Might have to split this out into another thread, because there is an amazing coincidence between my model of luni-solar driven QBO and a similar application to the Chandler wobble. Grumbine thinks the Chandler wobble is solar+planetary influence, but I argue that it is solar+lunar influence based on the following calculation, which I described on my blog yesterday:
[Possible Luni-Solar Tidal Mechanism for the Chandler Wobble](http://contextearth.com/2016/01/27/possible-luni-solar-tidal-mechanism-for-the-chandler-wobble/)
What I wrote there as a bottom-line is that:
*This idea essentially relates that the modulation of the yearly solar orbit (365.242 days) with the draconic (or nodal) lunar month of 27.21222 days sets up the perfect cyclic forcing for the 433 +/- 1.1 days Chandler wobble period.*
*Think in terms of the maximum declination of (1) the moon with respect to the equator along with (2) the maximum declination of the sun with respect to the equator. For (1) this happens once every ½ of the 27.2122 day nodal cycle or 13.60611 days and for (2) this happens twice a year (once for the southern hemisphere summer and once for the northern hemisphere summer).*
*Calculating this out, the closest aliased value is 2π(365.242/13.606)−52π = 5.303 rads/year, equivalent to a period of 432.77 days. That is close to the generally accepted value of 433 days for the wobble*.
![view](https://imageshack.com/i/p7JQ4s7og)
The way to think about this is of a spinning top (the Earth) being tugged at by a force that is simultaneously rotating obliquely about that axis (the Moon). If the Moon was strictly rotating concentrically about the equator, no wobble would be observed. But since the Moon follows a path with varying levels of declination about the equator, one would naively imagine that this would induce a slight wobbling force to the Earth's axis. That's what they refer to as a nutation, i.e. a wobbling rotation. Yet this idea is largely dismissed in the literature, suggesting that the Chandler wobble period is a "free" rotation arising more from a resonance condition involving the density and other characteristics of the Earth.
I would take their word for it if the wobble period of 432.7 days calculated from a first-principle trig argument didn't align so closely with the measured 433 days. Don't you hate when that happens? :)
So is the wobble forced or is it free? Grumbine says the former but lays it on solar+planetary forcing, whereas I think the 433 day period points to the forcing as predominately solar+lunar. I posted a comment to Grumbine's blog and will see how he responds.

If I found an annoying hum in some arbitrary electrical signal and wanted to rule out the AC power line voltage as the source, all I would have to do is show that the frequency of that hum was not 60 Hz. If the hum did happen to measure as 60 Hz, I still couldn't prove it was due to the line, but some other method would be needed to verify that it wasn't the line.

That's what will need to be done to debunk the lunar-forced Chandler wobble model. And for that matter, the QBO model. The ball is no longer in my court :)

Comment Source:Now that I put the predicted 432.77 day period for the Chandler wobble on the table, the focus should be on to prove that it is not a Lunar forcing which provides the wobble pacemaker signal.
Here is a histogram of citations of the Chandler wobble period from the year 2000 to now based on statistics from Google scholar. Search string "chandler wobble" "430 days", etc.
<pre>
period count
--- ---
430 85
431 11
432 22
433 101
434 22
435 85
436 11
</pre>
The weighted average is 432.78 days.
---
If I found an annoying hum in some arbitrary electrical signal and wanted to rule out the AC power line voltage as the source, all I would have to do is show that the frequency of that hum was not 60 Hz. If the hum did happen to measure as 60 Hz, I still couldn't prove it was due to the line, but some other method would be needed to verify that *it wasn't* the line.
That's what will need to be done to debunk the lunar-forced Chandler wobble model. And for that matter, the QBO model. The ball is no longer in my court :)

I dont know what you mean by closest aliased value, why are you deducting 52π ? -but whatsoever
I could imagine that all the computations of how the Chandler wobble
might arise (if it does) from planetary motions is already very wellknown to planetary scientists.

I just looked at wikipedia

The existence of Earth's free nutation was predicted by Isaac Newton in Corollaries 20 to 22 of Proposition 66, Book 1 of the Philosophiæ Naturalis Principia Mathematica, and by Leonhard Euler in 1765 as part of his studies of the dynamics of rotating bodies. Based on the known ellipticity of the Earth, Euler predicted that it would have a period of 305 days. Several astronomers searched for motions with this period, but none was found. Chandler's contribution was to look for motions at any possible period; once the Chandler wobble was observed, the difference between its period and the one predicted by Euler was explained by Simon Newcomb as being caused by the non-rigidity of the Earth.

and it seems already newton and Euler were thinking that the wobble is mostly a planetary feature.
Cant imagine that there are no preciser calculations.

Maybe the abstracts on Grumbines page and also that description on Wikipedia:

One promising theory for the source of the wobble was proposed in 2001 by Richard Gross at the Jet Propulsion Laboratory managed by the California Institute of Technology. He used angular momentum models of the atmosphere and the oceans in computer simulations to show that from 1985 to 1996, the Chandler wobble was excited by a combination of atmospheric and oceanic processes, with the dominant excitation mechanism being ocean‐bottom pressure fluctuations. Gross found that two-thirds of the "wobble" was caused by fluctuating pressure on the seabed, which, in turn, is caused by changes in the circulation of the oceans caused by variations in temperature, salinity, and wind. The remaining third is due to atmospheric fluctuations.[5]

are misleading and the calculations are not based on the atmossphere alone.

by the way. I cant see why

"it is unlikely that lunar periods could be produced by anything other than the lunar tidal potential."

excludes lunar cycles.

Comment Source:>the closest aliased value is 2π(365.242/13.606)−52π = 5.303 rads/year,
I dont know what you mean by closest aliased value, why are you deducting 52π ? -but whatsoever
I could imagine that all the computations of how the Chandler wobble
might arise (if it does) from planetary motions is already very wellknown to planetary scientists.
I just looked at wikipedia
>The existence of Earth's free nutation was predicted by Isaac Newton in Corollaries 20 to 22 of Proposition 66, Book 1 of the Philosophiæ Naturalis Principia Mathematica, and by Leonhard Euler in 1765 as part of his studies of the dynamics of rotating bodies. Based on the known ellipticity of the Earth, Euler predicted that it would have a period of 305 days. Several astronomers searched for motions with this period, but none was found. Chandler's contribution was to look for motions at any possible period; once the Chandler wobble was observed, the difference between its period and the one predicted by Euler was explained by Simon Newcomb as being caused by the non-rigidity of the Earth.
and it seems already newton and Euler were thinking that the wobble is mostly a planetary feature.
Cant imagine that there are no preciser calculations.
Maybe the abstracts on Grumbines page and also that description on Wikipedia:
>One promising theory for the source of the wobble was proposed in 2001 by Richard Gross at the Jet Propulsion Laboratory managed by the California Institute of Technology. He used angular momentum models of the atmosphere and the oceans in computer simulations to show that from 1985 to 1996, the Chandler wobble was excited by a combination of atmospheric and oceanic processes, with the dominant excitation mechanism being ocean‐bottom pressure fluctuations. Gross found that two-thirds of the "wobble" was caused by fluctuating pressure on the seabed, which, in turn, is caused by changes in the circulation of the oceans caused by variations in temperature, salinity, and wind. The remaining third is due to atmospheric fluctuations.[5]
are misleading and the calculations are not based on the atmossphere alone.
by the way. I cant see why
>"it is unlikely that lunar periods could be produced by anything other than the lunar tidal potential."
excludes lunar cycles.

This is the lowest frequency Fourier series component of the convolution of the Draconic fortnightly sine wave (13.606 day period) with a half-yearly pulse train. In this sense, the closest aliased value is equivalent to the lowest since only low frequency values would show enough sustained force to overcome the inertia of the Earth's mass. See comment #105 upthread for a complete derivation applied to QBO. The same analysis applies to the Chandler wobble.

By the way 52π is the same as 26·2π. If the inertial sensitivity was high enough then the higher frequency components, corresponding to shifts of 25·2π and 24·2π would show up as well. In fact, these higher frequency factors are clearly detectable in comment #110 for the machine learning analysis of the QBO time series.

As far as the math is concerned, I believe this is basic analysis. I took both analog and digital signal processing courses in my junior year of college, and then Fourier optics later. The equivalent to the aliasing in the spatial domain would be a Moire pattern. The basic methods to deduce aliasing are well known. Perhaps I learned practical applications of this early enough in my education that it is second nature to me, but I can't speak for others.

"-but whatsoever I could imagine that all the computations of how the Chandler wobble might arise (if it does) from planetary motions is already very wellknown to planetary scientists."

I would think that we should be able to find explicit citations for where the Chandler wobble frequency aligns with the lunar nodal month. Perhaps we start with Cassini's laws and how the Draconic month may apply.

"are misleading and the calculations are not based on the atmossphere alone."

That is a transitive observation if you consider that the QBO itself (an atmospheric process) is linked to the Draconic month, as I showed earlier. The theory of Gross may be essentially chasing its own tail!

by the way. I cant see why

"it is unlikely that lunar periods could be produced by anything other than the lunar tidal potential."
excludes lunar cycles.

That's what Lindzen said, not me. The lunar tidal potential is cyclical so that is a lunar cycle. There is an expression in English that says if something "walks like a duck and quacks like a duck, then it is a duck" . That's essentially what Lindzen was claiming -- if any evidence of the lunar tidal cycle shows up in measurements of atmospheric characteristics such as wind, then it has to be of lunar origin. Alas, Lindzen could never find it, but he obviously must not have considered aliasing.

Comment Source:> "I dont know what you mean by closest aliased value, why are you deducting 52π ? "
This is the lowest frequency Fourier series component of the convolution of the Draconic fortnightly sine wave (13.606 day period) with a half-yearly pulse train. In this sense, the closest aliased value is equivalent to the lowest since only low frequency values would show enough sustained force to overcome the inertia of the Earth's mass. See [comment #105 upthread](/#Comment_15124) for a complete derivation applied to QBO. The same analysis applies to the Chandler wobble.
By the way 52π is the same as 26·2π. If the inertial sensitivity was high enough then the higher frequency components, corresponding to shifts of 25·2π and 24·2π would show up as well. In fact, these higher frequency factors are clearly detectable in [comment #110](#Comment_15134) for the machine learning analysis of the QBO time series.
As far as the math is concerned, I believe this is basic analysis. I took both analog and digital signal processing courses in my junior year of college, and then Fourier optics later. The equivalent to the aliasing in the spatial domain would be a Moire pattern. The basic methods to deduce aliasing are well known. Perhaps I learned practical applications of this early enough in my education that it is second nature to me, but I can't speak for others.
>"-but whatsoever I could imagine that all the computations of how the Chandler wobble might arise (if it does) from planetary motions is already very wellknown to planetary scientists."
I would think that we should be able to find explicit citations for where the Chandler wobble frequency aligns with the lunar nodal month. Perhaps we start with Cassini's laws and how the Draconic month may apply.
http://farside.ph.utexas.edu/teaching/celestial/Celestial/node76.html
http://farside.ph.utexas.edu/teaching/celestial/Celestial/node74.html#sprec
You mention Gross's arguments
> "are misleading and the calculations are not based on the atmossphere alone."
That is a transitive observation if you consider that the QBO itself (an atmospheric process) is linked to the Draconic month, as I showed earlier. The theory of Gross may be essentially chasing its own tail!
>by the way. I cant see why
>> "it is unlikely that lunar periods could be produced by anything other than the lunar tidal potential."
>excludes lunar cycles.
That's what Lindzen said, not me. The lunar tidal potential is cyclical so that is a lunar cycle. There is an expression in English that says if something *"walks like a duck and quacks like a duck, then it is a duck"* . That's essentially what Lindzen was claiming -- if any evidence of the lunar tidal cycle shows up in measurements of atmospheric characteristics such as wind, then it has to be of lunar origin. Alas, Lindzen could never find it, but he obviously must not have considered aliasing.

Since the lunar QBO model works so precisely, one would imagine that these same physical principles would work for other phenomena; in this case the Chandler wobble.

Very straightforward to do a simple fit using the Excel solver, assuming a yearly sinusoidal signal combined additively with a Chandler signal of varying period, amplitude and phase. For the figure below, the solver picked a frequency extremely close to the predicted aliased Draconic lunar signal (see the numbers in red).

The fit was based on a short training interval, and then extrapolated over the longer time series. I also included the aliased harmonics that are in the QBO signal, but those are at the 1% level of amplitude so do not seem to be significant.

Amazing that the agreement for this case is at the 5th decimal place in terms of precision! This fit says the Chandler wobble period is 432.74 days.

A spurious coincidence, or is the moon the pacemaker of the Chandler wobble, just as it is for the QBO?

Comment Source:Since the lunar QBO model works so precisely, one would imagine that these same physical principles would work for other phenomena; in this case the Chandler wobble.
Very straightforward to do a simple fit using the Excel solver, assuming a yearly sinusoidal signal combined additively with a Chandler signal of varying period, amplitude and phase. For the figure below, the solver picked a frequency extremely close to the predicted aliased Draconic lunar signal (see the numbers in red).
![cw](http://imageshack.com/a/img922/9128/U1BKZz.png)
The fit was based on a short training interval, and then extrapolated over the longer time series. I also included the aliased harmonics that are in the QBO signal, but those are at the 1% level of amplitude so do not seem to be significant.
Amazing that the agreement for this case is at the 5th decimal place in terms of precision! This fit says the Chandler wobble period is 432.74 days.
A spurious coincidence, or is the moon the pacemaker of the Chandler wobble, just as it is for the QBO?

"-but whatsoever I could imagine that all the computations of how the Chandler wobble might arise (if it does) from planetary motions is already very wellknown to planetary scientists."

I always remember an anecdote that my father would occasionally tell me. Whenever he had a promising idea, he would routinely hear this from his engineering colleagues : "If it's such a good idea, why hasn't anybody thought of it before???"

Then we shared a laugh at the logic fail. Although that was before the phrase logic fail was invented :)

Comment Source:I was thinking about what Nad said:
>"-but whatsoever I could imagine that all the computations of how the Chandler wobble might arise (if it does) from planetary motions is already very wellknown to planetary scientists."
I always remember an anecdote that my father would occasionally tell me. Whenever he had a promising idea, he would routinely hear this from his engineering colleagues : <b>*"If it's such a good idea, why hasn't anybody thought of it before???"*</b>
Then we shared a laugh at the logic fail. Although that was before the phrase logic fail was invented :)

The extent of the Chandler wobble is a change of ~9 meters in which the rotational axis intersects the Earth's surface. Once this wobble is in motion, all it takes is a reinforcing pulse to keep it going. The kinetic energy in the wobble is built up over many years, and any dissipation via friction, etc must be minimal.

It's not that puzzling that the declination cycle of the Moon with respect to the Earth's axis was dismissed, as the period is only 27 days -- but then if you consider a nonlinear mechanism involving an extra push from the 1/2-year seasonal solar declination cycle, the 433 day period emerges in the Moire pattern.

Doing a literature search on this possible mechanism, I found papers by N. Sidorenkov (an AGW denier) who tries to deduce the wobble period by putting together various lunar cycles (see here). But his number is not spot on, and not nearly as cogent an argument that I am putting forward.

Comment Source:The extent of the Chandler wobble is a change of ~9 meters in which the rotational axis intersects the Earth's surface. Once this wobble is in motion, all it takes is a reinforcing pulse to keep it going. The kinetic energy in the wobble is built up over many years, and any dissipation via friction, etc must be minimal.
It's not that puzzling that the declination cycle of the Moon with respect to the Earth's axis was dismissed, as the period is only 27 days -- but then if you consider a nonlinear mechanism involving an extra push from the 1/2-year seasonal solar declination cycle, the 433 day period emerges in the Moire pattern.
![cw](http://contextearth.com/wp-content/uploads/2016/01/CW_draconic.gif)
Doing a literature search on this possible mechanism, I found papers by N. Sidorenkov (an AGW denier) who tries to deduce the wobble period by putting together various lunar cycles (see [here](http://contextearth.com/2014/06/17/the-qbom/)). But his number is not spot on, and not nearly as cogent an argument that I am putting forward.

"No one should carry an umbrella just because the moon is rising," Kohyama said. Instead, this effect could be used to test climate models ...

The author is being diplomatic in his wording. He knows that unfortunately, it will wreak havoc on the premises of the current climate models, which don't include any lunar forcing. Consider that for the QBO, it is ALL lunar forcing driven. That's why Lindzen got derailed in his QBO theory ...

Kohyama, Wallace - "Classical tidal theory, e.g., as presented in Lindzen and Chapman [1969] predicts the existence of a linear relationship between perturbations in pressure and RH. "

Lindzen could never find the pressure differentials that the moon was applying to the stratosphere, strong enough to get the QBO cycle in motion.

Comment Source:Thanks to @RGatess, here is very recent substantiation of the effect that the lunar gravitational tides can have on the tropical atmosphere ["Rainfall variations induced by the lunar gravitational atmospheric tide and their implications for the relationship between tropical rainfall and humidity", Kohyama, Wallace, UWashington](http://onlinelibrary.wiley.com/doi/10.1002/2015GL067342/full)
A [press clipping](http://phys.org/news/2016-01-phase-moon-affects-amount-rainfall.html) quotes the author
> "No one should carry an umbrella just because the moon is rising," Kohyama said. Instead, this effect could be used to test climate models ...
The author is being diplomatic in his wording. He knows that unfortunately, it will wreak havoc on the premises of the current climate models, which don't include any lunar forcing. Consider that for the QBO, it is ALL lunar forcing driven. That's why Lindzen got derailed in his QBO theory ...
> Kohyama, Wallace - "Classical tidal theory, e.g., as presented in Lindzen and Chapman [1969] predicts the existence of a linear relationship between perturbations in pressure and RH. "
Lindzen could never find the pressure differentials that the moon was applying to the stratosphere, strong enough to get the QBO cycle in motion.

Eventually a consensus emerges; sometimes it takes time, other times it is more immediate, especially if many people are involved in maintaining the charade.

One of my favorite movies to watch is Capricorn One, which is a recreation of a moon landing hoax scenario.

Turning the tables, why has is it not been revealed strongly that the moon's orbit has more of an impact on climate measures than we are lead to believe?
A research group at JPL wrote up a proposal for a project looking at the moon's influence on climate. Unfortunately, the proposal got rejected and one of the project leads quit and started an independent project: http://MoonClimate.org/ From their web site:

All the evidence I find points to a connection, yet it is always so easy to pull out the correlation≠causation card. In fact, there is little we can do to prove anything with respect to Earth Sciences, largely because we can't do a controlled experiment. All we can do is keep fitting data and making predictions and waiting for matching results (as if that helps any). The hoax on us, at least until the tide shifts :)

Comment Source:This was a fun piece to write
http://contextearth.com/2016/02/03/if-the-glove-dont-fit/
Pondering the interpretation of correlation and causation.
It's a timely post in more ways than one. A recent study making the rounds concerns how difficult it is to maintain an elaborate hoax involving many people over time:
http://bigthink.com/natalie-shoemaker/whats-the-probability-that-the-moon-landing-was-all-a-hoax-one-man-has-done-the-math
Eventually a consensus emerges; sometimes it takes time, other times it is more immediate, especially if many people are involved in maintaining the charade.
One of my favorite movies to watch is Capricorn One, which is a recreation of a moon landing hoax scenario.
Turning the tables, why has is it not been revealed strongly that the moon's orbit has more of an impact on climate measures than we are lead to believe?
A research group at JPL wrote up a proposal for a project looking at the moon's influence on climate. Unfortunately, the proposal got rejected and one of the project leads quit and started an independent project: [http://MoonClimate.org/](http://moonclimate.org/) From their web site:
![moonclimate](http://imageshack.com/a/img922/9382/HGeAKc.gif)
All the evidence I find points to a connection, yet it is always so easy to pull out the correlation≠causation card. In fact, there is little we can do to *prove* anything with respect to Earth Sciences, largely because we can't do a controlled experiment. All we can do is keep fitting data and making predictions and waiting for matching results (as if that helps any). The hoax on us, at least until the tide shifts :)

An interesting and longstanding question pertaining to the Chandler wobble pertains to an apparent 180 degree phase inversion of the wobble measure occurring around 1930. The data does get more noisy before 1960, but this inversion behavior looks pretty clear.

The phase reversal occurs over the course of a couple of years, so doesn't look like a gradual change in phase that you would see if the frequency wasn't locked to the real fundamental.

The first line in each set is the yearly signal component. This doesn't really change in magnitude (9.2 vs 9.14) and the phase change is slight and possibly in the margin of error.

The second line is the Chandler wobble frequency component. This is slightly smaller in magnitude prior to 1930, but shows the phase change of 2.82 radians which is nearly the $\pi$ radians seen in a perfect phase inversion.

The last pair is a long-period oscillation (85 year) used to help in the fit.

If the Chandler wobble is possibly caused by lunar declination extremes (which sounds rather intuitive), then a phase reversal would require the extremes to switch to midpoints. That doesn't make intuitive sense. The only way it would sound plausible is if the equatorial bulge suddenly changed in scale at 1930, such that the gravitational torque of the moon at the equator became stronger than the polar torque.

As the Chandler wobble is a slight effect, and the fact that the behavior is sitting along a knife-edge in forcing magnitude required, then this may indeed be a factor responsible for the phase reversal.

Comment Source:An interesting and longstanding question pertaining to the Chandler wobble pertains to an apparent 180 degree phase inversion of the wobble measure occurring around 1930. The data does get more noisy before 1960, but this inversion behavior looks pretty clear.
![cw](http://imageshack.com/a/img922/592/Hj3qwi.png)
The phase reversal occurs over the course of a couple of years, so doesn't look like a gradual change in phase that you would see if the frequency wasn't locked to the real fundamental.
This is the modeled waveform, after 1960 and then before 1930
<pre>
+ 9.20 * sin(2*pi*t/1+1.447)
+ 15.0 * sin(2*pi*t/1.185+0.51966)
+ 3.35 * sin(2*pi*t/85-2.0013)
+ 9.14 * sin(2*pi*t/1+1.224)
+ 12.8 * sin(2*pi*t/1.185-2.3043)
+ 3.22 * sin(2*pi*t/85-0.53978)
</pre>
The first line in each set is the yearly signal component. This doesn't really change in magnitude (9.2 vs 9.14) and the phase change is slight and possibly in the margin of error.
The second line is the Chandler wobble frequency component. This is slightly smaller in magnitude prior to 1930, but shows the phase change of 2.82 radians which is nearly the $\pi$ radians seen in a perfect phase inversion.
The last pair is a long-period oscillation (85 year) used to help in the fit.
If the Chandler wobble is possibly caused by lunar declination extremes (which sounds rather intuitive), then a phase reversal would require the extremes to switch to midpoints. That doesn't make intuitive sense. The only way it would sound plausible is if the equatorial bulge suddenly changed in scale at 1930, such that the gravitational torque of the moon at the equator became stronger than the polar torque.
As the Chandler wobble is a slight effect, and the fact that the behavior is sitting along a knife-edge in forcing magnitude required, then this may indeed be a factor responsible for the phase reversal.

A. Einstein's gravitational waves were long conjectured to exist. No one could see the signal because it was buried in too much noise. When the noise sources were gradually removed and differential detection approaches were optimized, scientists could finally see the GW signal emerge. They knew what they wanted to observe and what Einstein said would exist, and finally found it.

B. Atmospheric tides, similar to the well known oceanic tides, have long been conjectured to exist. The QBO may be a manifestation of such a tide. The strongest tidal force is when a long-term pressure gradient is built-up arising from an optimal positioning of the moon and sun. The issue has been that the time-scales were wrong and the QBO showed a longer period than what was expected from tidal forces. Yet there is a time scale of luni-solar behavior which is reasonable, and now that we know what we are looking for, it is not so hard to explain QBO. So the lunar forced model of QBO works well with respect to the observed data.

Comment Source:The analogy is this:
A. Einstein's gravitational waves were long conjectured to exist. No one could see the signal because it was buried in too much noise. When the noise sources were gradually removed and differential detection approaches were optimized, scientists could finally see the GW signal emerge. They knew what they wanted to observe and what Einstein said would exist, and finally found it.
B. Atmospheric tides, similar to the well known oceanic tides, have long been conjectured to exist. The QBO may be a manifestation of such a tide. The strongest tidal force is when a long-term pressure gradient is built-up arising from an optimal positioning of the moon and sun. The issue has been that the time-scales were wrong and the QBO showed a longer period than what was expected from tidal forces. Yet there is a time scale of luni-solar behavior which is reasonable, and now that we know what we are looking for, it is not so hard to explain QBO. So the lunar forced model of QBO works well with respect to the observed data.
http://contextearth.com/2016/02/13/qbo-model-validation/

Obviously the fit is good because once you start fiddling with arbitrarily shaped periodic components, you can match anything. Perhaps a good example of over-fitting.

Comment Source:Here is a paper on teasing what appear to be non-linear oscillations out of the QBO.
[1] S. Pulkkinen, “Nonlinear kernel density principal component analysis with application to climate data,” Statistics and Computing, vol. 26, no. 1–2, pp. 471–492, 2016. [pdf](https://www.researchgate.net/profile/Seppo_Pulkkinen/publication/269289713_Nonlinear_kernel_density_principal_component_analysis_with_application_to_climate_data/links/558c2e5c08ae1f30aa8098a8.pdf)
Obviously the fit is good because once you start fiddling with arbitrarily shaped periodic components, you can match anything. Perhaps a good example of over-fitting.

Since Richard Lindzen is the originator of the "consensus" QBO theory, I try to keep up with what he is saying in research and opinion pieces that pop up every once in a while. As he has now retired into an emeritus position, he has tended to provide more opinion than substance.

His latest piece just about made my skin crawl. I found this interview today, wherein he says "We increasingly are getting students who are not as sophisticated as they used to be."

This is the context:

"William Frezza: Dick, as you see young scientists coming up in the field, do they find themselves very energised by this topic?

Richard Lindzen: It’s an interesting question – we’re getting applications from a different group. When I started teaching, there was a real split in graduate school – you had undergraduates studying meteorology with the intention of becoming weathermen. The graduate students in fields like meteorology came from physics and math, you know, because these are hard problems in physics and math.

William Frezza: They’re interesting, yeah.

Richard Lindzen: Physics and math no longer have an overflow, as student interest shifted to, you know, law, business, you know, so on. We increasingly are getting students who are not as sophisticated as they used to be. ..."

Yea, like MIT doesn't attract the best and the brightest, no matter the discipline. Sheez.

Comment Source:Since Richard Lindzen is the originator of the "consensus" QBO theory, I try to keep up with what he is saying in research and opinion pieces that pop up every once in a while. As he has now retired into an emeritus position, he has tended to provide more opinion than substance.
His latest piece just about made my skin crawl. I found [this interview](http://cliscep.com/2016/02/23/catastrophe-was-the-narrative-from-the-beginning-says-lindzen/#comment-1755) today, wherein he says *"We increasingly are getting students who are not as sophisticated as they used to be."*
This is the context:
>"William Frezza: Dick, as you see young scientists coming up in the field, do they find themselves very energised by this topic?
>Richard Lindzen: It’s an interesting question – we’re getting applications from a different group. When I started teaching, there was a real split in graduate school – you had undergraduates studying meteorology with the intention of becoming weathermen. The graduate students in fields like meteorology came from physics and math, you know, because these are hard problems in physics and math.
>William Frezza: They’re interesting, yeah.
>Richard Lindzen: Physics and math no longer have an overflow, as student interest shifted to, you know, law, business, you know, so on. We increasingly are getting students who are not as sophisticated as they used to be. ..."
Yea, like MIT doesn't attract the best and the brightest, no matter the discipline. Sheez.

As climate scientist Ray Perrehumbert said in a 2012 lecture to the American Geophysical Union:

“It’s OK to be wrong, and [Richard] is a smart person, but most people don’t really understand that one way of using your intelligence is to spin ever more clever ways of deceiving yourself. … He has made a career of being wrong in interesting ways about climate science.”

Sarah then fact-checks some of Lindzen's most recent claims to show where he has gone wrong.

Interesting that she claims that Lindzen apparently gives these interviews every election cycle to provide fodder to the right-wing politicians.

Comment Source:Response by [Sarah Sloat of inverse.com](https://www.inverse.com/article/11643-climate-change-denying-mit-prof-richard-lindzen-is-suddenly-popular-still-wrong) to the Richard Lindzen interview
>As climate scientist Ray Perrehumbert said in a 2012 lecture to the American Geophysical Union:
>> “It’s OK to be wrong, and [Richard] is a smart person, but most people don’t really understand that one way of using your intelligence is to spin ever more clever ways of deceiving yourself. … He has made a career of being wrong in interesting ways about climate science.”
Sarah then fact-checks some of Lindzen's most recent claims to show where he has gone wrong.
Interesting that she claims that Lindzen apparently gives these interviews every election cycle to provide fodder to the right-wing politicians.

Different combination of colors on this fit to the second-derivative of QBO. Blue and red is a better contrast than the blue and green I was using before.

In this 60 year interval there are about 125 peaks and 125 valleys that align fairly well, simply by applying the lunar long-period gravitational forcing factors.

It looks good, but there might be an additional factor that could improve the fit. My guess it wouldn't be something that improves the alignment of the peaks but rather a factor that modulates the strength of the peaks.

Comment Source:Different combination of colors on this fit to the second-derivative of QBO. Blue and red is a better contrast than the blue and green I was using before.
In this 60 year interval there are about 125 peaks and 125 valleys that align fairly well, simply by applying the lunar long-period gravitational forcing factors.
![fit](http://imagizer.imageshack.us/a/img921/2124/k0xw17.png)
It looks good, but there might be an additional factor that could improve the fit. My guess it wouldn't be something that improves the alignment of the peaks but rather a factor that modulates the strength of the peaks.

An interesting possibility for incrementally improving the excellent fit of the QBO is to consider a saturation function for the peaks and valleys. The QBO wind speeds give the impression that they limit out at a certain value. One way to model this is to apply a saturating factor such as

$ QBO_s(t) = \frac{QBO(t)}{1+k|QBO(t)|} $

This is essentially an application of a gradual diminishing returns factor so once the value in the denominator achieves a certain value it cancels the numerator. I realize that is a bit of a heuristic but the physics behind wind does show a limiting factor and this may be the simplest means to represent that behavior.

The improvement in fit is about 0.05 in the correlation coefficient. Here is the second derivative alignment, which is based on the fit to the QBO.

Realize that this two difference functions in a row making it a very sensitive measure of edge detection and alignment.

Comment Source:An interesting possibility for incrementally improving the excellent fit of the QBO is to consider a saturation function for the peaks and valleys. The QBO wind speeds give the impression that they limit out at a certain value. One way to model this is to apply a saturating factor such as
$ QBO_s(t) = \frac{QBO(t)}{1+k|QBO(t)|} $
This is essentially an application of a gradual diminishing returns factor so once the value in the denominator achieves a certain value it cancels the numerator. I realize that is a bit of a heuristic but the physics behind wind does show a limiting factor and this may be the simplest means to represent that behavior.
The improvement in fit is about 0.05 in the correlation coefficient. Here is the second derivative alignment, which is based on the fit to the QBO.
![fit](http://imageshack.com/a/img922/2119/ea0m2v.gif)
Realize that this two difference functions in a row making it a very sensitive measure of edge detection and alignment.

Reading through it, you get the impression that Lindzen's entire theory is analogous to a Rudyard Kipling "just-so story". Layer after layer of rationalizations or explanations are added to the initial hypothesis until something works. By working, the system starts oscillating. He doesn't say how the exact period comes about, but I guess that isn't considered important after Lindzen declared victory.

Comment Source:Interesting piece of self-serving fluff by Richard Lindzen from 1987 recounting the history of his formulation of the theory behind QBO (abbreviated LH [1]).
[PDF](http://journals.ametsoc.org/doi/pdf/10.1175/1520-0477%281987%29068%3C0329%3AOTDOTT%3E2.0.CO%3B2)
Reading through it, you get the impression that Lindzen's entire theory is analogous to a Rudyard Kipling ["just-so story"](https://en.wikipedia.org/wiki/Just-so_story). Layer after layer of rationalizations or explanations are added to the initial hypothesis until something works. By working, the system starts oscillating. He doesn't say how the exact period comes about, but I guess that isn't considered important after Lindzen declared victory.
Lindzen also cites another crazy AGW denier for contributing to the QBO theory, Murry Salby -- the guy who claims that the [excess atmospheric CO2 is natural and coming from the oceans](http://www.skepticalscience.com/Murry-Salby-CO2-rise-natural.htm).
Yet there is some promise in the concluding paragraph, where Lindzen writes:
![lastPar](http://imageshack.com/a/img921/8458/bGb1w1.png)
I guess that isn't too far from what we are doing in the Azimuth project.
[1] R. S. Lindzen and J. R. Holton, “A theory of the quasi-biennial oscillation,” Journal of the Atmospheric Sciences, vol. 25, no. 6, pp. 1095–1107, 1968.

Two fits of QBO using the same sinusoidal tidal factors but differing slightly in amplitude and phase.
The upper is the 30 hPa time series and the lower is the 70 hPa :

The idea is that the lower altitude is a spatio-temporal dispersion of the upper altitude values. The dispersion is not extremely strong as the periodic factors are robustly maintained, and so it is mainly an amplitude reduction and phase shift impacting each of the Fourier series coefficients differently.

This is further substantiation that these specific periods are precisely determined by matching to the aliased lunisolar tidal cycles.

Comment Source:Two fits of QBO using the same sinusoidal tidal factors but differing slightly in amplitude and phase.
The upper is the 30 hPa time series and the lower is the 70 hPa :
![two](http://imagizer.imageshack.us/a/img923/121/a3UZ7y.png)
The idea is that the lower altitude is a spatio-temporal dispersion of the upper altitude values. The dispersion is not extremely strong as the periodic factors are robustly maintained, and so it is mainly an amplitude reduction and phase shift impacting each of the Fourier series coefficients differently.
This is further substantiation that these specific periods are precisely determined by matching to the aliased lunisolar tidal cycles.

A set of all the available QBO data sets along with fitted models, using the same aliased lunisolar tidal factors, only adjusted to get the phase and amplitude to match. The data corresponds to 10 hPa, 15 hPa, 20 hPa, 30 hPa, 40 hPa, 50 hPa, 70 hPa average barometric pressure levels -- i.e. higher to lower altitudes.

It's extremely difficult for one model to fit all 7 sets of data if there was any randomness to the behavior.

Data between the years 1953 and 1955 are more likely to be extrapolated:

Comment Source:A set of all the available QBO data sets along with fitted models, using the same aliased lunisolar tidal factors, only adjusted to get the phase and amplitude to match. The data corresponds to 10 hPa, 15 hPa, 20 hPa, 30 hPa, 40 hPa, 50 hPa, 70 hPa average barometric pressure levels -- i.e. higher to lower altitudes.
![all](http://imageshack.com/a/img922/8199/jlhllp.png)
It's extremely difficult for one model to fit all 7 sets of data if there was any randomness to the behavior.
Data between the years 1953 and 1955 are more likely to be extrapolated:
![data](http://imageshack.com/a/img921/2048/JugebZ.gif)

Comment Source:If the moon can cause this:
![tide](http://esl-seminar-jacob.wikispaces.umb.edu/file/view/fundy-tides-comparison%5B4%5D.jpg/553642088/fundy-tides-comparison%5B4%5D.jpg)
what else can it do?
That's the overriding question and one that can only be answered by observational data, since we don't have a controlled experiment at our disposal. .
Yet when the numbers match up so perfectly, the correlation has to be taken seriously. That is the theme of my latest blog post here:
http://contextearth.com/2016/03/06/forced-versus-natural-response-not-a-secret

Here is another fit over each of the QBO time-series, except it uses only data from 1955 to 1985 as the training interval (the yellow shaded region). The model after 1985 is a pure projection, which can be used to validate the goodness of the fit, thus reducing possible over-fitting errors.

Comment Source:Here is another fit over each of the QBO time-series, except it uses only data from 1955 to 1985 as the training interval (the yellow shaded region). The model after 1985 is a pure projection, which can be used to validate the goodness of the fit, thus reducing possible over-fitting errors.
![fit](http://imageshack.com/a/img922/1239/Y1eDoi.png)

This recent review paper by Mayr & Lee has an interesting slant at how seasonal modulation can occur.

It is clear that a strong and temporally-narrow seasonal modulation against the lunar gravitational forcing is the driving stimulus behind the QBO. Yet actually "seeing" this effect is no easy task, and models such as Mayr's are promising physical abstractions to start with.

Comment Source:This recent review paper by Mayr & Lee has an interesting slant at how seasonal modulation can occur.
![mayr](http://imageshack.com/a/img921/534/RzgHRk.gif)
It is clear that a strong and temporally-narrow seasonal modulation against the lunar gravitational forcing is the driving stimulus behind the QBO. Yet actually "seeing" this effect is no easy task, and models such as Mayr's are promising physical abstractions to start with.

It takes time to read through all the published research on the QBO. One name that frequently comes up is Murry Salby, who has written a couple of comprehensive textbooks on atmospheric physics and several papers on QBO.

Salby, Murry, and Patrick Callaghan. "Connection between the solar cycle and the QBO: the missing link." Journal of Climate 13.14 (2000): 2652-2662.

The Australian judge dismissed his case. Salby's history is detailed here by John Mashey.

Between Lindzen, Salby, and others who have studied QBO in detail, such as William Gray, you have to wonder if their contrarian AGW views have to do with their apprehension over the challenges of climate science? Salby most recently said that he doesn't even accept that the 400 PPM (and rising) atmospheric CO2 concentration is from burning fossil fuel. Disputing that fact is way on the fringe of skepticism.

Reading their papers on QBO and knowing their background, I tend to have my own apprehension over their claims to understand the behavior, knowing full well that they don't accept the physics of AGW.

Comment Source:It takes time to read through all the published research on the QBO. One name that frequently comes up is Murry Salby, who has written a couple of comprehensive textbooks on atmospheric physics and several papers on QBO.
> Salby, Murry, and Patrick Callaghan. "Connection between the solar cycle and the QBO: the missing link." Journal of Climate 13.14 (2000): 2652-2662.
> Salby, Murry L., and Patrick F. Callaghan. "Relationship of the quasi‐biennial oscillation to the stratospheric signature of the solar cycle." Journal of Geophysical Research: Atmospheres 111.D6 (2006).
Yet, Salby is constantly embroiled in controversy over his work. In the last few months, he tried to sue his most recent University employer for allegedly firing him over his contrarian AGW views:
http://www.theaustralian.com.au/higher-education/climate-change-critic-murry-salby-loses-case-against-university/news-story/31cc4d13e601e32acbf383cd6996eb6b
The Australian judge dismissed his case. Salby's history is detailed [here](http://www.desmogblog.com/2013/07/12/murry-salby-galileo-bozo-or-p-t-barnum) by John Mashey.
Between Lindzen, Salby, and others who have studied QBO in detail, such as [William Gray](http://www.westword.com/news/the-skeptic-5089763), you have to wonder if their contrarian AGW views have to do with their apprehension over the challenges of climate science? Salby most recently said that he doesn't even accept that the 400 PPM (and rising) atmospheric CO2 concentration is from burning fossil fuel. Disputing that fact is way on the fringe of skepticism.
Reading their papers on QBO and knowing their background, I tend to have my own apprehension over their claims to understand the behavior, knowing full well that they don't accept the physics of AGW.

Some more notes: One of the reasons that the stratospheric winds are strongest at the equator is that the coriolis force (and its dissipative reaction) drops to zero exactly at the equator. By isolating and dropping those cross-terms we can simplify the model with respect to another spatial dimension. BTW, the term stratosphere comes from stratify, which was meant to point out how this particular atmospheric layer does not interact with other layers.

With that simplification, the only mechanism to counteract the lunisolar tidal forcing is viscous dissipation. The result is a clean waveform that is simple to fit with the aliased Fourier series coefficients.

Comment Source:Some more notes: One of the reasons that the stratospheric winds are strongest at the equator is that the coriolis force (and its dissipative reaction) drops to zero exactly at the equator. By isolating and dropping those cross-terms we can simplify the model with respect to another spatial dimension. BTW, the term stratosphere comes from stratify, which was meant to point out how this particular atmospheric layer does not interact with other layers.
With that simplification, the only mechanism to counteract the lunisolar tidal forcing is viscous dissipation. The result is a clean waveform that is simple to fit with the aliased Fourier series coefficients.

If the wave equation is to be effective in modeling a forced behavior then certain invariant properties would need to be observed.

$ f''(t) + \omega_0^2 f(t) = F(t) $

So if we split this into two parts

$ f''(t) \approx k_1 F(t) $

$ \omega_0^2 f(t) \approx k_2 F(t) $

I have been applying multiple linear regression to fit the wave equation via either of the above two forms

So if we combine these two and see how well the Fourier series coefficients align -- keeping care to compensate for the $\omega^2$ scaling factor after taking the second derivative -- the linear result should be:

$ \frac{f''(t)}{f(t)} = \omega_0^2 k_1/k_2 $

and indeed !

$R^2$ is 0.997

Remarkably, I did not apply any filtering to the QBO signal.

Comment Source:If the wave equation is to be effective in modeling a forced behavior then certain invariant properties would need to be observed.
$ f''(t) + \omega_0^2 f(t) = F(t) $
So if we split this into two parts
$ f''(t) \approx k_1 F(t) $
$ \omega_0^2 f(t) \approx k_2 F(t) $
I have been applying multiple linear regression to fit the wave equation via either of the above two forms
So if we combine these two and see how well the Fourier series coefficients align -- keeping care to compensate for the $\omega^2$ scaling factor after taking the second derivative -- the linear result should be:
$ \frac{f''(t)}{f(t)} = \omega_0^2 k_1/k_2 $
and indeed !
![qboRatio](http://imageshack.com/a/img922/4609/97fAOK.png)
$R^2$ is 0.997
Remarkably, I did not apply any filtering to the QBO signal.

John was asking about summarizing the progress. I can only talk this through subjectively at the moment.

Here goes:

If a 60 Hz signal was observed in some output waveform, the no-brainer response is to assume first that it has something to do with an AC voltage bleeding through the wall outlet or transmitted through some nearby power lines.

An engineer/scientist/technician's first response wouldn't be that a 60 Hz signal was due to an internal resonance, or a Philip Glass recording, or a whale, or an alien communication from deep space. That would be silly because none of these are parsimonious explanations for an otherwise common behavior.

Yet I assert that kind of parsimonious explanation is what we're seeing -- and that's in direct contradiction to Richard Lindzen's theory of QBO. Lindzen formulated a model for QBO that assumes some worldwide resonance creates the oscillations via atmospheric waves. To make matters more complicated, researchers that followed his lead developed a variety of mechanisms to generate the resonance, for example, by tweaking the GCMs until the QBO period was observed.

But since I contend that the QBO is more readily explained by a seasonally aliased forcing of the lunisolar tides, all the previously considered mechanisms are nearly as useless as the ones for misidentifying a 60 Hz hum. Unless we can identify an originating behavior which appears fundamentally correct, the risk is that the entire foundation is fragile, and whatever models are built on top of it is as flimsy as a house of cards.

A strong refutation requires strong substantiating evidence, and that's what I have been working on since I wrote a short whitepaper on this topic back in October of last year. I placed a PDF version of that paper on ARXIV as part of the process of submitting to potential APS journals, but it was quickly removed by the site moderators. They emailed me with the veiled threat that:

Further attempts to submit "Lunar Tidal Potential Forcing for QBO" will result in the loss of your submission privileges.

...

Since that time, I have been gingerly walking on eggshells in trying to figure out a path forward. So I'm in a kind of holding pattern in trying not to make matters worse. I'm not working on this full-time so the only good thing that does come out of it is to be able to incrementally come up with other pieces of evidence, such as the correlation in my previous comment.

I guess this is one of the dangers of going down the independent research rabbit hole, which was the intent of the ENSO code project. Its all well and good and great fun while we are all flailing about with the research itself. But what happens if we really find something innovative?

This process reminds me of the Robert Redford movie The Candidate from 1972. The plot centers around a presidential election for a manufactured candidate. The closing line after Redford's character Bill McKay is announced the winner is:

Bill McKay: "What do we do now?"

That's where the next challenge begins because there is no cookbook recipe to follow. I would know what to do if I was still working at IBM Watson, because the skids are already greased for publication, etc. But I am not part of the earth sciences inner circle and so have no real path forward.

Comment Source:I placed a combination of the previous comment and some thoughts on inferring forcing on my blog:
[http://ContextEarth.com/2016/03/21/inferring-forced-response-from-qbo-wave-equation/](http://contextearth.com/2016/03/21/inferring-forced-response-from-qbo-wave-equation/)
John was asking about summarizing the progress. I can only talk this through subjectively at the moment.
Here goes:
If a 60 Hz signal was observed in some output waveform, the no-brainer response is to assume first that it has something to do with an AC voltage bleeding through the wall outlet or transmitted through some nearby power lines.
An engineer/scientist/technician's first response wouldn't be that a 60 Hz signal was due to an internal resonance, or a Philip Glass recording, or a whale, or an alien communication from deep space. That would be silly because none of these are parsimonious explanations for an otherwise common behavior.
Yet I assert that kind of parsimonious explanation is what we're seeing -- and that's in direct contradiction to Richard Lindzen's [theory of QBO](https://en.wikipedia.org/wiki/Quasi-biennial_oscillation). Lindzen formulated a model for QBO that assumes some worldwide resonance creates the oscillations via atmospheric waves. To make matters more complicated, researchers that followed his lead developed a variety of mechanisms to generate the resonance, for example, by tweaking the GCMs until the QBO period was observed.
But since I contend that the QBO is more readily explained by a seasonally aliased forcing of the lunisolar tides, all the previously considered mechanisms are nearly as useless as the ones for misidentifying a 60 Hz hum. Unless we can identify an *originating* behavior which appears fundamentally correct, the risk is that the entire foundation is fragile, and whatever models are built on top of it is as flimsy as a house of cards.
A strong refutation requires strong substantiating evidence, and that's what I have been working on since I wrote a short whitepaper on this topic back in [October of last year](http://contextearth.com/2015/10/22/pukites-model-of-the-quasi-biennial-oscillation/qbo_paper/). I placed a PDF version of that paper on ARXIV as part of the process of submitting to potential APS journals, but it was quickly removed by the site moderators. They emailed me with the veiled threat that:
> On Tue, Oct 27, 2015 at 2:39 PM, arXiv Moderation <moderation@arxiv.org> wrote:
> ...
> Further attempts to submit "Lunar Tidal Potential Forcing for QBO" will result in the loss of your submission privileges.
> ...
Since that time, I have been gingerly walking on eggshells in trying to figure out a path forward. So I'm in a kind of holding pattern in trying not to make matters worse. I'm not working on this full-time so the only good thing that does come out of it is to be able to incrementally come up with other pieces of evidence, such as the correlation in my previous comment.
I guess this is one of the dangers of going down the independent research rabbit hole, which was the intent of the ENSO code project. Its all well and good and great fun while we are all flailing about with the research itself. But what happens if we really find something innovative?
This process reminds me of the Robert Redford movie The Candidate from 1972. The plot centers around a presidential election for a manufactured candidate. The closing line after Redford's character Bill McKay is announced the winner is:
> Bill McKay: "What do we do now?"
That's where the next challenge begins because there is no cookbook recipe to follow. I would know what to do if I was still working at IBM Watson, because the skids are already greased for publication, etc. But I am not part of the earth sciences inner circle and so have no real path forward.

Your submission has been removed upon a notice from our moderators, who determined it inappropriate for arXiv. Please send to a conventional journal instead for the necessary reviews. Our moderators are not reviewers and do not provide reviews with their decisions.

arXiv is a forum for professional members of the scientific community. Our moderators have requested that you respond to the following query before submitting any other articles:

Do you have a conventional publication record? In what field? Please provide us with a current list of publications.

What is the precise nature of your institutional affiliation?

I did simultaneously submit to an APS journal, but since my arXiv link was now dead (see below), I wasn't sure what to do next. Per their suggestions, I updated my credentials on my registration profile, pointing to my Google Scholar page for a list of publications.
So when I resubmitted again, that's when they bullied me.

After thinking about the first response, I should have read between the lines and realized that they just didn't want to deal with the paper (or me?).

What makes the system broken is that certain American Physical Society journals suggest you submit a paper through arXiv first, and then you provide them the arXiv link in the submission form. So they are being disingenuous when they asked me to submit to a "conventional journal" instead.

Comment Source:Jim, This is what they sent me for reasons:
> Your submission has been removed upon a notice from our moderators, who determined it inappropriate for arXiv. Please send to a conventional journal instead for the necessary reviews. Our moderators are not reviewers and do not provide reviews with their decisions.
> arXiv is a forum for professional members of the scientific community. Our moderators have requested that you respond to the following query before submitting any other articles:
> 1. Do you have a conventional publication record? In what field? Please provide us with a current list of publications.
> 2. What is the precise nature of your institutional affiliation?
I did simultaneously submit to an APS journal, but since my arXiv link was now dead (see below), I wasn't sure what to do next. Per their suggestions, I updated my credentials on my registration profile, pointing to my Google Scholar page for a list of publications.
So when I resubmitted again, that's when they bullied me.
After thinking about the first response, I should have read between the lines and realized that they just didn't want to deal with the paper (or me?).
What makes the system broken is that certain American Physical Society journals suggest you submit a paper through arXiv first, and then you provide them the arXiv link in the submission form. So they are being disingenuous when they asked me to submit to a "conventional journal" instead.

I should be working on preparing taxes, but this new correlation has got me preoccupied.

What I did was apply the QBO aliased lunar tidal model to another measure that seems pretty obvious -- long term monthly time series data of sea-level height (SLH), in this particular case tidal gauge readings in Sydney harbor (I wrote about correlating Sydney data to ENSO before -- post 1, post 2 ).

The key here is that I used the second-derivative of the tidal data for the multiple regression fit:

This is remarkable as it applies the as-is QBO factors to Sydney training data from 1940 to 1970. That is, the parameters are derived from the critical aliased lunisolar periods used to optimize the QBO fit.

I don't know why I didn't try this earlier, since it's kind of obvious that whatever lunisolar forces may drive the QBO will certainly drive the sea-level height.
Yet I can see why this has been overlooked in the past, since the precise seasonal aliasing of the lunar periods is something that is not intuitive.

Here is another screenshot with an extra low-pass filter

Remember, this is not the fast (daily) tidal changes as seen below, but what is averaged over the course of a month. Clearly some aliasing will occur simply due to the math of artificial aliasing (i.e. a lunar month is shorter than a calendar month), but this still has vast implications for how the data needs to be modeled.

And I think it will help fill in the details for an ENSO model, as the tidal gauge data also shows a hidden correlation to the SOI measure:

I will get to my taxes eventually.

Comment Source:I should be working on preparing taxes, but this new correlation has got me preoccupied.
What I did was apply the QBO aliased lunar tidal model to another measure that seems pretty obvious -- long term monthly time series data of sea-level height (SLH), in this particular case tidal gauge readings in Sydney harbor (I wrote about correlating Sydney data to ENSO before -- [post 1](http://contextearth.com/2014/09/16/using-tidal-gauges-to-estimate-enso/), [post 2](http://contextearth.com/2014/09/21/an-enso-predictor-based-on-a-tide-gauge-data-model/) ).
The key here is that I used the second-derivative of the tidal data for the multiple regression fit:
![SLH](http://imageshack.com/a/img923/9424/HWAuzb.png)
This is remarkable as it applies the *as-is* QBO factors to Sydney training data from 1940 to 1970. That is, the parameters are derived from the critical aliased lunisolar periods used to optimize the QBO fit.
The second derivative allows us to fit against [a wave equation model](http://contextearth.com/2015/11/17/the-math-of-seasonal-aliasing/).
I don't know why I didn't try this earlier, since it's kind of obvious that whatever lunisolar forces may drive the QBO will certainly drive the sea-level height.
Yet I can see why this has been overlooked in the past, since the precise seasonal aliasing of the lunar periods is something that is not intuitive.
Here is another screenshot with an extra low-pass filter
![SLH2](http://imageshack.com/a/img923/8066/31Joec.png)
Remember, this is not the fast (daily) tidal changes as seen below, but what is averaged over the course of a month. Clearly some aliasing will occur simply due to the math of artificial aliasing (i.e. a lunar month is shorter than a calendar month), but this still has vast implications for how the data needs to be modeled.
![pic](http://www.cdn.sciencebuddies.org/Files/6426/7/high-tide-low-tide.jpg)
And I think it will help fill in the details for an ENSO model, as the tidal gauge data also shows a hidden correlation to the [SOI measure](http://contextearth.com/2014/09/16/using-tidal-gauges-to-estimate-enso/):
![soi tides](http://imagizer.imageshack.us/a/img912/9310/ag13Vs.gif)
I will get to my taxes eventually.

I realize this is the QBO thread, but now I found an even more amazing correlation that the extended SLH readings from Sydney Harbor have with the SOI. This is important because the data for SOI is not uniformly high-quality over the years.

This is the noisy SLH signal that we are dealing with:

What I found was that the yearly and biannual lunisolar signals are cross-modulated by ENSO, and if these form the basis functions for the tidal SLH, then the SLH and SOI time series correlate amazingly well.

In the first grouping, look at where the errors in the tidal gauge SLH modulation occur, big spikes at 1905 and 1950 -- at the same intervals where I have problems with the ENSO model, see the green shaded region below.

To explain the excursions, either the model is wrong or the data is wrong. It's possible that the tidal gauge SLH data is telling us that the official SOI readings are erroneous at these points.

Comment Source:I realize this is the QBO thread, but now I found an even more amazing correlation that the extended SLH readings from Sydney Harbor have with the SOI. This is important because the data for SOI is not uniformly high-quality over the years.
This is the noisy SLH signal that we are dealing with:
![](http://imageshack.com/a/img922/9671/EukeGP.png)
What I found was that the yearly and biannual lunisolar signals are cross-modulated by ENSO, and if these form the basis functions for the tidal SLH, then the SLH and SOI time series correlate amazingly well.
Y(t) = yearly and seasonal biannual signal
LOD(t) = long-term angular moment changes (in Length-of-day) that has correlation with temperature
TSI(t) = solar (sunspot) variation
CO2(t) = AGW component
SOI(t) = southern index oscillation
Trying to extract the SOI signal from the SLH signal
(1) SOI(t) = SLH(t) - Y(t) * ( 1 + k*SOI(t) ) - LOD(t) - TSI(t) - CO2(t)
This is admittedly tricky because the cross-terms introduce an automatic correlation. So I'm aware and very sensitive to this issue but its worth the risk to work through it.
![](http://imageshack.com/a/img922/196/wZkibh.png)
Expanded version along the training interval, the two downward dips at 1983 and 1998 are the big El Ninos.
![](http://imageshack.com/a/img921/4931/Tp4zhw.png)
I next grouped the cross-terms on the SOI side (compare to (1) above)
(2) SLH(t) = SOI(t) + Y(t) * ( 1 + k*SOI(t) ) + LOD(t) + TSI(t) + CO2(t)
![](http://imageshack.com/a/img922/8008/iqtLDZ.png)
![](http://imageshack.com/a/img922/1946/1ULR25.png)
In the first grouping, look at where the errors in the tidal gauge SLH modulation occur, big spikes at 1905 and 1950 -- at the same intervals where I have problems with the ENSO model, see the green shaded region below.
![](http://imageshack.com/a/img921/7158/szkiON.png)
To explain the excursions, either the model is wrong or the data is wrong. It's possible that the tidal gauge SLH data is telling us that the official SOI readings are erroneous at these points.

The arXiv needs to moderate submissions to avoid being overwhelmed by a flood of crackpots: there are lots of physics crackpots, and many are crazier than you can possibly imagine, and very eager to put papers on the arXiv. Unfortunately, drawing the line between crackpots and unorthodox but reasonable theorists is very tough.

It will be hard for Paul to ever get a paper on the arXiv now that one has been rejected. The way to avoid being rejected in the first place is to write in a very careful way. If Paul had asked me for help in writing the paper, I could have helped with that. Academia has certain rules, somewhat unfair, that serve to delimit its boundaries. There are certain things about Paul's writing that set off alarm bells.

Comment Source:Jim wrote:
> They don't do reviews but they moderate? Would anybody from the Azimuth project have the mileage to help sort out this nonsense?
There are lots of arguments about arXiv moderation. See for example:
* Sabine Hossenfelder, [Does the arXiv censor submissions?](http://backreaction.blogspot.com/2016/01/does-arxiv-censor-submissions.html), _Backreaction_, 28 January 2016.
The arXiv needs to moderate submissions to avoid being overwhelmed by a flood of crackpots: there are lots of physics crackpots, and many are crazier than you can possibly imagine, and very eager to put papers on the arXiv. Unfortunately, drawing the line between crackpots and unorthodox but reasonable theorists is very tough.
It will be hard for Paul to ever get a paper on the arXiv now that one has been rejected. The way to avoid being rejected in the first place is to write in a very careful way. If Paul had asked me for help in writing the paper, I could have helped with that. Academia has certain rules, somewhat unfair, that serve to delimit its boundaries. There are certain things about Paul's writing that set off alarm bells.

Another tidal gauge SLH data set with a long history (1900-2000) is the one from Auckland, NZ. There were a few missing data points so I interpolated over those.

This shows almost identical behavior as the Sydney Harbor set:

After training on the Aukland data, the error excursions at 1905 and 1950 are still there.

Comment Source:Another tidal gauge SLH data set with a long history (1900-2000) is the one from Auckland, NZ. There were a few missing data points so I interpolated over those.
This shows almost identical behavior as the Sydney Harbor set:
![aukland](http://imageshack.com/a/img922/6162/tuOn1s.png)
After training on the Aukland data, the error excursions at 1905 and 1950 are still there.

It's a little sad about arXiv. Maybe it was always intended to be in the way described, but it certainly flies against the airstream of "putting anything and everything out there", and letting the readership sift and decide what's important. It's really not that difficult to do, especially with RSS/Atom subscriptions.

There could be some filtering of results by limiting an arXiv alter ego to strictly reproducible submissions, taking "reproducible research" quite literally. There is a movement in Statistics where people provide not only the capability in LaTeX to regenerate the paper, but, using something standard like R, to repeat all the calculations in the paper from datasets, also provided along with the paper. Naturally, this would limit arXiv alter ago to data-derived papers, but I can't see how you get any quality control on pure Maths or perhaps Theoretical Physics without eyeballs on the paper and, probably, several.

The reaction could be to set up said arXiv alter ago in some way. To the degree production and refereeing costs are inhibiting submissions and sharing of results, especially sound, but "not new" intermediate results means, in my opinion, the world will see more vehicles like Sci-Hub. What's strange to me is that academics don't properly perceive this to be what it is, a DISRUPTION of their standard model of practice by technology and by a subset of the public which is scientifically and mathematically semi-literate but which finds the criteria for acceptance in official science difficult to understand and, sometimes (and with cause), downright distasteful.

Facts are, I fear academics is shunning a segment of scientific and mathematical practice which, in history, has been important. It does not matter if the contributors were (engineer) Guy Stewart Callendar in his work on carbonic acid, or legions of amateur astronomers, or amateur meteorologists, or amateur ornithologists, or people who take water samples for official use in their local streams. The place where this gets difficult is the place where, because of the antics of the Science Denier crowd, academics scream "Shields up!" and shut out everyone other than in the Priesthood.

I would say it is key, in an environment of shrinking funding, especially for experimental science, to encourage and train this kind of participation. There are highly successful projects which have done this kind of thing, that I am developing data analysis tools to support. See https://www.whoi.edu/news-release/BuzzardsBay

Comment Source:@John Baez, @Jim Studdard,
It's a little sad about arXiv. Maybe it was always intended to be in the way described, but it certainly flies against the airstream of "putting anything and everything out there", and letting the readership sift and decide what's important. It's really not that difficult to do, especially with RSS/Atom subscriptions.
There could be some filtering of results by limiting an arXiv alter ego to strictly reproducible submissions, taking "reproducible research" quite literally. There is a movement in Statistics where people provide not only the capability in LaTeX to regenerate the paper, but, using something standard like R, to repeat all the calculations in the paper from datasets, also provided along with the paper. Naturally, this would limit arXiv alter ago to data-derived papers, but I can't see how you get any quality control on pure Maths or perhaps Theoretical Physics without eyeballs on the paper and, probably, several.
The reaction could be to set up said arXiv alter ago in some way. To the degree production and refereeing costs are inhibiting submissions and sharing of results, especially sound, but "not new" intermediate results means, in my opinion, the world will see more vehicles like Sci-Hub. What's strange to me is that academics don't properly perceive this to be what it is, a DISRUPTION of their standard model of practice by technology and by a subset of the public which is scientifically and mathematically semi-literate but which finds the criteria for acceptance in official science difficult to understand and, sometimes (and with cause), downright distasteful.
Facts are, I fear academics is shunning a segment of scientific and mathematical practice which, in history, has been important. It does not matter if the contributors were (engineer) Guy Stewart Callendar in his work on carbonic acid, or legions of amateur astronomers, or amateur meteorologists, or amateur ornithologists, or people who take water samples for official use in their local streams. The place where this gets difficult is the place where, because of the antics of the Science Denier crowd, academics scream "Shields up!" and shut out everyone other than in the Priesthood.
I would say it is key, in an environment of shrinking funding, especially for experimental science, to encourage and train this kind of participation. There are highly successful projects which have done this kind of thing, that I am developing data analysis tools to support. See https://www.whoi.edu/news-release/BuzzardsBay

Comment Source:What would [Seth Carlo Chandler](https://en.wikipedia.org/wiki/Seth_Carlo_Chandler) do today?
In his day, he was a total outsider scientist, doing it only as a hobby.
I don't understand why the Chandler wobble isn't simply explained via aliasing with the nodal/draconic cycle of the moon.
http://contextearth.com/2016/01/27/possible-luni-solar-tidal-mechanism-for-the-chandler-wobble/
![wobble](http://imageshack.com/a/img922/9128/U1BKZz.png)

Comment Source:There was this renowned climate scientist Bill Gray who was considered the authority on predicting hurricanes, and who applied the [behavior of QBO to his hurricane prediction algorithms](https://en.wikipedia.org/wiki/William_M._Gray#Research).
Yet he was also an AGW denier and claimed that AGW was a hoax. A Washington Post article from 2006 revealed :
> "He has had to put his own money, more than $100,000, into keeping his research going. ...
> Gray believes in the obs. The observations. Direct measurements. Numerical models can't be trusted. Equation pushers with fancy computers aren't the equals of scientists who fly into hurricanes."
So why do the observations of QBO numerically agree with that of the lunar cycle?
http://contextearth.com/2016/02/13/qbo-model-validation/
Must be due to that fancy old PC which costed a couple hundred bucks.

That WaPo article really tells you the full story on scientists such as Lindzen and Gray who have studied QBO for so long:

"Of all the skeptics, MIT's Richard Lindzen probably has the most credibility among mainstream scientists, who acknowledge that he's doing serious research on the subject. Lindzen contends that water vapor and clouds, which will increase in a warmer world because of higher rates of evaporation, create "negative feedbacks" that counter the warming trend. "The only reason the models get such a big response is that, in models, the most important greenhouse substances, which are water vapor and clouds, act to take anything man does and make it worse," he says. Observations show otherwise, he says.

Lindzen argues that the climate models can't be right, because we've already raised CO2 and methane dramatically, and the planet simply hasn't warmed that much. But Isaac Held, a NOAA modeler, says Lindzen is jumping the gun, because the greenhouse gases take time -- decades, centuries -- to have their full impact. Indeed, we've already made a "commitment" to warming. We couldn't stop global warming at this point if we closed every factory and curbed every car. The mainstream argument is that we could minimize the increase, and reduce the risk of a dangerous, unstable, white-knuckle climate change.

Held studied under Lindzen years ago and considers him a friend and a smart scientist -- but highly contrarian.

"There're people like [Lindzen] in every field of science. There are always people in the fringes. They're attracted to the fringe . . . It may be as simple as, how do you prove you're smarter than everyone else? You don't do that by being part of the consensus," Held says.

The most vocal partisans in the climate change debate often describe their opponents as part of a conspiracy, of sorts. Both sides think the other side has a monetary or political incentive to skew the data. But there are people in this battle who fervently believe in what they say. Bill Gray says he takes no fossil-fuel money. He's simply sick and tired of squishy-minded hand-wringing equation-pushing computer jocks who've never flown into a hurricane!

Gray has his own conspiracy theory. He has made a list of 15 reasons for the global warming hysteria. The list includes the need to come up with an enemy after the end of the Cold War, and the desire among scientists, government leaders and environmentalists to find a political cause that would enable them to "organize, propagandize, force conformity and exercise political influence. Big world government could best lead (and control) us to a better world!"

Gray admits that he has a dark take on human nature: "I have a demonic view on this." "

Wow, read the whole article, that was almost 10 years ago. Can't believe that these are the scientists that were considered the experts on topics such as QBO!

Comment Source:That WaPo article really tells you the full story on scientists such as Lindzen and Gray who have studied QBO for so long:
>"Of all the skeptics, MIT's Richard Lindzen probably has the most credibility among mainstream scientists, who acknowledge that he's doing serious research on the subject. Lindzen contends that water vapor and clouds, which will increase in a warmer world because of higher rates of evaporation, create "negative feedbacks" that counter the warming trend. "The only reason the models get such a big response is that, in models, the most important greenhouse substances, which are water vapor and clouds, act to take anything man does and make it worse," he says. Observations show otherwise, he says.
> Lindzen argues that the climate models can't be right, because we've already raised CO2 and methane dramatically, and the planet simply hasn't warmed that much. But Isaac Held, a NOAA modeler, says Lindzen is jumping the gun, because the greenhouse gases take time -- decades, centuries -- to have their full impact. Indeed, we've already made a "commitment" to warming. We couldn't stop global warming at this point if we closed every factory and curbed every car. The mainstream argument is that we could minimize the increase, and reduce the risk of a dangerous, unstable, white-knuckle climate change.
> Held studied under Lindzen years ago and considers him a friend and a smart scientist -- but highly contrarian.
> "There're people like [Lindzen] in every field of science. There are always people in the fringes. They're attracted to the fringe . . . It may be as simple as, how do you prove you're smarter than everyone else? You don't do that by being part of the consensus," Held says.
> The most vocal partisans in the climate change debate often describe their opponents as part of a conspiracy, of sorts. Both sides think the other side has a monetary or political incentive to skew the data. But there are people in this battle who fervently believe in what they say. Bill Gray says he takes no fossil-fuel money. He's simply sick and tired of squishy-minded hand-wringing equation-pushing computer jocks who've never flown into a hurricane!
> Gray has his own conspiracy theory. He has made a list of 15 reasons for the global warming hysteria. The list includes the need to come up with an enemy after the end of the Cold War, and the desire among scientists, government leaders and environmentalists to find a political cause that would enable them to "organize, propagandize, force conformity and exercise political influence. Big world government could best lead (and control) us to a better world!"
> Gray admits that he has a dark take on human nature: "I have a demonic view on this." "
Wow, read the [whole article](http://www.washingtonpost.com/wp-dyn/content/article/2006/05/23/AR2006052301305.html), that was almost 10 years ago. Can't believe that these are the scientists that were considered the experts on topics such as QBO!